correct_cartesianelliptic.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def coeff():\n",
    "    for i in range(1,n):\n",
    "        for j in range(1,m):\n",
    "            A[i,j]=2.0/(h*h)+2.0/(k*k)\n",
    "            B[i,j]=1.0/(h*h)\n",
    "            C[i,j]=1.0/(h*h)\n",
    "            D[i,j]=1.0/(k*k)\n",
    "            E[i,j]=1.0/(k*k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gauss():\n",
    "    for k in range(1,p):\n",
    "        for i in range(1,n):\n",
    "            for j in range(1,m):\n",
    "                U[i,j]=(B[i,j]*U[i-1,j]+C[i,j]*U[i+1,j]+D[i,j]*U[i,j-1]+E[i,j]*U[i,j+1])/A[i,j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max1= 0.0009986410251308087\n",
      "[[0.00000000e+00 0.00000000e+00 0.00000000e+00 ... 0.00000000e+00\n",
      "  0.00000000e+00 0.00000000e+00]\n",
      " [0.00000000e+00 3.96707992e-04 7.94932591e-04 ... 2.93836713e-01\n",
      "  3.03821934e-01 3.14107591e-01]\n",
      " [0.00000000e+00 7.93397579e-04 1.58982669e-03 ... 5.87384639e-01\n",
      "  6.07344628e-01 6.27905195e-01]\n",
      " ...\n",
      " [0.00000000e+00 8.27290169e-04 1.65759510e-03 ... 5.87491488e-01\n",
      "  6.07398063e-01 6.27905195e-01]\n",
      " [0.00000000e+00 4.14032183e-04 8.29572376e-04 ... 2.93891326e-01\n",
      "  3.03849245e-01 3.14107591e-01]\n",
      " [0.00000000e+00 0.00000000e+00 0.00000000e+00 ... 0.00000000e+00\n",
      "  0.00000000e+00 0.00000000e+00]]\n",
      "iterations= 955\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa146f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "solution converge \n",
      "y = 0.0\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.000000 0.000000           0.000000\n",
      "0.020000 0.000000 0.000000           0.000000\n",
      "0.030000 0.000000 0.000000           0.000000\n",
      "0.040000 0.000000 0.000000           0.000000\n",
      "0.050000 0.000000 0.000000           0.000000\n",
      "0.060000 0.000000 0.000000           0.000000\n",
      "0.070000 0.000000 0.000000           0.000000\n",
      "0.080000 0.000000 0.000000           0.000000\n",
      "0.090000 0.000000 0.000000           0.000000\n",
      "0.100000 0.000000 0.000000           0.000000\n",
      "0.110000 0.000000 0.000000           0.000000\n",
      "0.120000 0.000000 0.000000           0.000000\n",
      "0.130000 0.000000 0.000000           0.000000\n",
      "0.140000 0.000000 0.000000           0.000000\n",
      "0.150000 0.000000 0.000000           0.000000\n",
      "0.160000 0.000000 0.000000           0.000000\n",
      "0.170000 0.000000 0.000000           0.000000\n",
      "0.180000 0.000000 0.000000           0.000000\n",
      "0.190000 0.000000 0.000000           0.000000\n",
      "0.200000 0.000000 0.000000           0.000000\n",
      "0.210000 0.000000 0.000000           0.000000\n",
      "0.220000 0.000000 0.000000           0.000000\n",
      "0.230000 0.000000 0.000000           0.000000\n",
      "0.240000 0.000000 0.000000           0.000000\n",
      "0.250000 0.000000 0.000000           0.000000\n",
      "0.260000 0.000000 0.000000           0.000000\n",
      "0.270000 0.000000 0.000000           0.000000\n",
      "0.280000 0.000000 0.000000           0.000000\n",
      "0.290000 0.000000 0.000000           0.000000\n",
      "0.300000 0.000000 0.000000           0.000000\n",
      "0.310000 0.000000 0.000000           0.000000\n",
      "0.320000 0.000000 0.000000           0.000000\n",
      "0.330000 0.000000 0.000000           0.000000\n",
      "0.340000 0.000000 0.000000           0.000000\n",
      "0.350000 0.000000 0.000000           0.000000\n",
      "0.360000 0.000000 0.000000           0.000000\n",
      "0.370000 0.000000 0.000000           0.000000\n",
      "0.380000 0.000000 0.000000           0.000000\n",
      "0.390000 0.000000 0.000000           0.000000\n",
      "0.400000 0.000000 0.000000           0.000000\n",
      "0.410000 0.000000 0.000000           0.000000\n",
      "0.420000 0.000000 0.000000           0.000000\n",
      "0.430000 0.000000 0.000000           0.000000\n",
      "0.440000 0.000000 0.000000           0.000000\n",
      "0.450000 0.000000 0.000000           0.000000\n",
      "0.460000 0.000000 0.000000           0.000000\n",
      "0.470000 0.000000 0.000000           0.000000\n",
      "0.480000 0.000000 0.000000           0.000000\n",
      "0.490000 0.000000 0.000000           0.000000\n",
      "0.500000 0.000000 0.000000           0.000000\n",
      "0.510000 0.000000 0.000000           0.000000\n",
      "0.520000 0.000000 0.000000           0.000000\n",
      "0.530000 0.000000 0.000000           0.000000\n",
      "0.540000 0.000000 0.000000           0.000000\n",
      "0.550000 0.000000 0.000000           0.000000\n",
      "0.560000 0.000000 0.000000           0.000000\n",
      "0.570000 0.000000 0.000000           0.000000\n",
      "0.580000 0.000000 0.000000           0.000000\n",
      "0.590000 0.000000 0.000000           0.000000\n",
      "0.600000 0.000000 0.000000           0.000000\n",
      "0.610000 0.000000 0.000000           0.000000\n",
      "0.620000 0.000000 0.000000           0.000000\n",
      "0.630000 0.000000 0.000000           0.000000\n",
      "0.640000 0.000000 0.000000           0.000000\n",
      "0.650000 0.000000 0.000000           0.000000\n",
      "0.660000 0.000000 0.000000           0.000000\n",
      "0.670000 0.000000 0.000000           0.000000\n",
      "0.680000 0.000000 0.000000           0.000000\n",
      "0.690000 0.000000 0.000000           0.000000\n",
      "0.700000 0.000000 0.000000           0.000000\n",
      "0.710000 0.000000 0.000000           0.000000\n",
      "0.720000 0.000000 0.000000           0.000000\n",
      "0.730000 0.000000 0.000000           0.000000\n",
      "0.740000 0.000000 0.000000           0.000000\n",
      "0.750000 0.000000 0.000000           0.000000\n",
      "0.760000 0.000000 0.000000           0.000000\n",
      "0.770000 0.000000 0.000000           0.000000\n",
      "0.780000 0.000000 0.000000           0.000000\n",
      "0.790000 0.000000 0.000000           0.000000\n",
      "0.800000 0.000000 0.000000           0.000000\n",
      "0.810000 0.000000 0.000000           0.000000\n",
      "0.820000 0.000000 0.000000           0.000000\n",
      "0.830000 0.000000 0.000000           0.000000\n",
      "0.840000 0.000000 0.000000           0.000000\n",
      "0.850000 0.000000 0.000000           0.000000\n",
      "0.860000 0.000000 0.000000           0.000000\n",
      "0.870000 0.000000 0.000000           0.000000\n",
      "0.880000 0.000000 0.000000           0.000000\n",
      "0.890000 0.000000 0.000000           0.000000\n",
      "0.900000 0.000000 0.000000           0.000000\n",
      "0.910000 0.000000 0.000000           0.000000\n",
      "0.920000 0.000000 0.000000           0.000000\n",
      "0.930000 0.000000 0.000000           0.000000\n",
      "0.940000 0.000000 0.000000           0.000000\n",
      "0.950000 0.000000 0.000000           0.000000\n",
      "0.960000 0.000000 0.000000           0.000000\n",
      "0.970000 0.000000 0.000000           0.000000\n",
      "0.980000 0.000000 0.000000           0.000000\n",
      "0.990000 0.000000 0.000000           0.000000\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.01\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.000855 0.000397           0.000458\n",
      "0.020000 0.001708 0.000793           0.000915\n",
      "0.030000 0.002560 0.001190           0.001371\n",
      "0.040000 0.003410 0.001585           0.001825\n",
      "0.050000 0.004256 0.001979           0.002277\n",
      "0.060000 0.005098 0.002372           0.002726\n",
      "0.070000 0.005935 0.002763           0.003172\n",
      "0.080000 0.006766 0.003151           0.003615\n",
      "0.090000 0.007591 0.003537           0.004054\n",
      "0.100000 0.008408 0.003919           0.004488\n",
      "0.110000 0.009216 0.004298           0.004918\n",
      "0.120000 0.010016 0.004673           0.005343\n",
      "0.130000 0.010805 0.005044           0.005762\n",
      "0.140000 0.011584 0.005410           0.006174\n",
      "0.150000 0.012352 0.005771           0.006581\n",
      "0.160000 0.013107 0.006127           0.006981\n",
      "0.170000 0.013850 0.006477           0.007373\n",
      "0.180000 0.014578 0.006820           0.007758\n",
      "0.190000 0.015293 0.007158           0.008135\n",
      "0.200000 0.015992 0.007488           0.008504\n",
      "0.210000 0.016676 0.007812           0.008864\n",
      "0.220000 0.017343 0.008128           0.009215\n",
      "0.230000 0.017993 0.008436           0.009556\n",
      "0.240000 0.018625 0.008737           0.009888\n",
      "0.250000 0.019239 0.009029           0.010210\n",
      "0.260000 0.019833 0.009312           0.010522\n",
      "0.270000 0.020409 0.009586           0.010822\n",
      "0.280000 0.020964 0.009851           0.011113\n",
      "0.290000 0.021498 0.010107           0.011391\n",
      "0.300000 0.022011 0.010352           0.011659\n",
      "0.310000 0.022503 0.010588           0.011914\n",
      "0.320000 0.022972 0.010814           0.012158\n",
      "0.330000 0.023419 0.011029           0.012390\n",
      "0.340000 0.023842 0.011233           0.012609\n",
      "0.350000 0.024242 0.011426           0.012816\n",
      "0.360000 0.024618 0.011609           0.013009\n",
      "0.370000 0.024970 0.011780           0.013190\n",
      "0.380000 0.025297 0.011939           0.013358\n",
      "0.390000 0.025599 0.012087           0.013512\n",
      "0.400000 0.025876 0.012223           0.013653\n",
      "0.410000 0.026127 0.012347           0.013780\n",
      "0.420000 0.026353 0.012459           0.013894\n",
      "0.430000 0.026552 0.012558           0.013994\n",
      "0.440000 0.026725 0.012646           0.014080\n",
      "0.450000 0.026872 0.012721           0.014152\n",
      "0.460000 0.026993 0.012783           0.014210\n",
      "0.470000 0.027087 0.012833           0.014254\n",
      "0.480000 0.027154 0.012870           0.014283\n",
      "0.490000 0.027194 0.012895           0.014299\n",
      "0.500000 0.027207 0.012907           0.014301\n",
      "0.510000 0.027194 0.012906           0.014288\n",
      "0.520000 0.027154 0.012892           0.014262\n",
      "0.530000 0.027087 0.012866           0.014221\n",
      "0.540000 0.026993 0.012827           0.014166\n",
      "0.550000 0.026872 0.012775           0.014098\n",
      "0.560000 0.026725 0.012710           0.014015\n",
      "0.570000 0.026552 0.012633           0.013919\n",
      "0.580000 0.026353 0.012544           0.013809\n",
      "0.590000 0.026127 0.012442           0.013686\n",
      "0.600000 0.025876 0.012327           0.013549\n",
      "0.610000 0.025599 0.012200           0.013399\n",
      "0.620000 0.025297 0.012061           0.013235\n",
      "0.630000 0.024970 0.011911           0.013059\n",
      "0.640000 0.024618 0.011748           0.012870\n",
      "0.650000 0.024242 0.011573           0.012669\n",
      "0.660000 0.023842 0.011387           0.012455\n",
      "0.670000 0.023419 0.011190           0.012229\n",
      "0.680000 0.022972 0.010981           0.011991\n",
      "0.690000 0.022503 0.010761           0.011741\n",
      "0.700000 0.022011 0.010531           0.011481\n",
      "0.710000 0.021498 0.010290           0.011209\n",
      "0.720000 0.020964 0.010038           0.010926\n",
      "0.730000 0.020409 0.009776           0.010632\n",
      "0.740000 0.019833 0.009505           0.010328\n",
      "0.750000 0.019239 0.009224           0.010015\n",
      "0.760000 0.018625 0.008933           0.009691\n",
      "0.770000 0.017993 0.008634           0.009359\n",
      "0.780000 0.017343 0.008326           0.009017\n",
      "0.790000 0.016676 0.008009           0.008667\n",
      "0.800000 0.015992 0.007684           0.008308\n",
      "0.810000 0.015293 0.007351           0.007942\n",
      "0.820000 0.014578 0.007011           0.007568\n",
      "0.830000 0.013850 0.006663           0.007187\n",
      "0.840000 0.013107 0.006309           0.006799\n",
      "0.850000 0.012352 0.005948           0.006404\n",
      "0.860000 0.011584 0.005580           0.006004\n",
      "0.870000 0.010805 0.005207           0.005598\n",
      "0.880000 0.010016 0.004829           0.005187\n",
      "0.890000 0.009216 0.004445           0.004771\n",
      "0.900000 0.008408 0.004057           0.004350\n",
      "0.910000 0.007591 0.003665           0.003926\n",
      "0.920000 0.006766 0.003268           0.003498\n",
      "0.930000 0.005935 0.002868           0.003067\n",
      "0.940000 0.005098 0.002464           0.002634\n",
      "0.950000 0.004256 0.002058           0.002198\n",
      "0.960000 0.003410 0.001650           0.001760\n",
      "0.970000 0.002560 0.001239           0.001321\n",
      "0.980000 0.001708 0.000827           0.000881\n",
      "0.990000 0.000855 0.000414           0.000441\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.02\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.001710 0.000795           0.000915\n",
      "0.020000 0.003418 0.001590           0.001829\n",
      "0.030000 0.005123 0.002384           0.002740\n",
      "0.040000 0.006823 0.003176           0.003647\n",
      "0.050000 0.008517 0.003966           0.004550\n",
      "0.060000 0.010201 0.004753           0.005448\n",
      "0.070000 0.011876 0.005536           0.006340\n",
      "0.080000 0.013539 0.006314           0.007225\n",
      "0.090000 0.015189 0.007087           0.008102\n",
      "0.100000 0.016823 0.007853           0.008970\n",
      "0.110000 0.018441 0.008612           0.009829\n",
      "0.120000 0.020041 0.009364           0.010677\n",
      "0.130000 0.021621 0.010107           0.011515\n",
      "0.140000 0.023180 0.010840           0.012340\n",
      "0.150000 0.024716 0.011564           0.013152\n",
      "0.160000 0.026227 0.012276           0.013951\n",
      "0.170000 0.027713 0.012978           0.014735\n",
      "0.180000 0.029171 0.013667           0.015505\n",
      "0.190000 0.030601 0.014343           0.016258\n",
      "0.200000 0.032000 0.015005           0.016995\n",
      "0.210000 0.033368 0.015653           0.017714\n",
      "0.220000 0.034702 0.016287           0.018416\n",
      "0.230000 0.036003 0.016905           0.019098\n",
      "0.240000 0.037268 0.017506           0.019761\n",
      "0.250000 0.038496 0.018091           0.020405\n",
      "0.260000 0.039686 0.018659           0.021027\n",
      "0.270000 0.040837 0.019208           0.021629\n",
      "0.280000 0.041948 0.019739           0.022209\n",
      "0.290000 0.043017 0.020251           0.022766\n",
      "0.300000 0.044044 0.020744           0.023300\n",
      "0.310000 0.045028 0.021216           0.023811\n",
      "0.320000 0.045967 0.021668           0.024298\n",
      "0.330000 0.046860 0.022099           0.024761\n",
      "0.340000 0.047708 0.022508           0.025199\n",
      "0.350000 0.048508 0.022896           0.025612\n",
      "0.360000 0.049260 0.023261           0.025999\n",
      "0.370000 0.049964 0.023603           0.026361\n",
      "0.380000 0.050619 0.023923           0.026696\n",
      "0.390000 0.051223 0.024219           0.027004\n",
      "0.400000 0.051777 0.024491           0.027286\n",
      "0.410000 0.052280 0.024740           0.027540\n",
      "0.420000 0.052731 0.024964           0.027767\n",
      "0.430000 0.053130 0.025164           0.027967\n",
      "0.440000 0.053477 0.025339           0.028139\n",
      "0.450000 0.053771 0.025489           0.028282\n",
      "0.460000 0.054012 0.025614           0.028398\n",
      "0.470000 0.054200 0.025714           0.028486\n",
      "0.480000 0.054334 0.025789           0.028546\n",
      "0.490000 0.054415 0.025838           0.028577\n",
      "0.500000 0.054442 0.025861           0.028580\n",
      "0.510000 0.054415 0.025860           0.028555\n",
      "0.520000 0.054334 0.025832           0.028502\n",
      "0.530000 0.054200 0.025779           0.028421\n",
      "0.540000 0.054012 0.025701           0.028311\n",
      "0.550000 0.053771 0.025597           0.028174\n",
      "0.560000 0.053477 0.025468           0.028009\n",
      "0.570000 0.053130 0.025313           0.027817\n",
      "0.580000 0.052731 0.025134           0.027597\n",
      "0.590000 0.052280 0.024929           0.027351\n",
      "0.600000 0.051777 0.024700           0.027077\n",
      "0.610000 0.051223 0.024446           0.026777\n",
      "0.620000 0.050619 0.024168           0.026451\n",
      "0.630000 0.049964 0.023865           0.026099\n",
      "0.640000 0.049260 0.023539           0.025721\n",
      "0.650000 0.048508 0.023189           0.025318\n",
      "0.660000 0.047708 0.022816           0.024891\n",
      "0.670000 0.046860 0.022421           0.024439\n",
      "0.680000 0.045967 0.022003           0.023964\n",
      "0.690000 0.045028 0.021562           0.023465\n",
      "0.700000 0.044044 0.021100           0.022944\n",
      "0.710000 0.043017 0.020617           0.022400\n",
      "0.720000 0.041948 0.020113           0.021835\n",
      "0.730000 0.040837 0.019589           0.021248\n",
      "0.740000 0.039686 0.019045           0.020641\n",
      "0.750000 0.038496 0.018482           0.020014\n",
      "0.760000 0.037268 0.017900           0.019368\n",
      "0.770000 0.036003 0.017299           0.018703\n",
      "0.780000 0.034702 0.016682           0.018021\n",
      "0.790000 0.033368 0.016047           0.017321\n",
      "0.800000 0.032000 0.015396           0.016604\n",
      "0.810000 0.030601 0.014729           0.015872\n",
      "0.820000 0.029171 0.014047           0.015124\n",
      "0.830000 0.027713 0.013351           0.014362\n",
      "0.840000 0.026227 0.012640           0.013587\n",
      "0.850000 0.024716 0.011917           0.012799\n",
      "0.860000 0.023180 0.011181           0.011999\n",
      "0.870000 0.021621 0.010434           0.011187\n",
      "0.880000 0.020041 0.009676           0.010366\n",
      "0.890000 0.018441 0.008907           0.009534\n",
      "0.900000 0.016823 0.008129           0.008694\n",
      "0.910000 0.015189 0.007342           0.007846\n",
      "0.920000 0.013539 0.006548           0.006991\n",
      "0.930000 0.011876 0.005746           0.006130\n",
      "0.940000 0.010201 0.004938           0.005263\n",
      "0.950000 0.008517 0.004124           0.004392\n",
      "0.960000 0.006823 0.003306           0.003518\n",
      "0.970000 0.005123 0.002483           0.002640\n",
      "0.980000 0.003418 0.001658           0.001761\n",
      "0.990000 0.001710 0.000830           0.000880\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.03\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.002567 0.001196           0.001371\n",
      "0.020000 0.005132 0.002392           0.002740\n",
      "0.030000 0.007691 0.003586           0.004105\n",
      "0.040000 0.010243 0.004778           0.005465\n",
      "0.050000 0.012785 0.005967           0.006819\n",
      "0.060000 0.015315 0.007150           0.008164\n",
      "0.070000 0.017829 0.008328           0.009501\n",
      "0.080000 0.020325 0.009498           0.010827\n",
      "0.090000 0.022802 0.010661           0.012141\n",
      "0.100000 0.025256 0.011813           0.013442\n",
      "0.110000 0.027685 0.012956           0.014729\n",
      "0.120000 0.030087 0.014086           0.016001\n",
      "0.130000 0.032459 0.015203           0.017255\n",
      "0.140000 0.034799 0.016307           0.018492\n",
      "0.150000 0.037104 0.017395           0.019710\n",
      "0.160000 0.039374 0.018467           0.020907\n",
      "0.170000 0.041604 0.019522           0.022082\n",
      "0.180000 0.043793 0.020558           0.023235\n",
      "0.190000 0.045939 0.021575           0.024364\n",
      "0.200000 0.048039 0.022572           0.025468\n",
      "0.210000 0.050093 0.023547           0.026546\n",
      "0.220000 0.052096 0.024500           0.027597\n",
      "0.230000 0.054049 0.025429           0.028620\n",
      "0.240000 0.055948 0.026334           0.029614\n",
      "0.250000 0.057792 0.027214           0.030578\n",
      "0.260000 0.059578 0.028067           0.031511\n",
      "0.270000 0.061306 0.028894           0.032412\n",
      "0.280000 0.062974 0.029693           0.033281\n",
      "0.290000 0.064579 0.030463           0.034116\n",
      "0.300000 0.066121 0.031204           0.034917\n",
      "0.310000 0.067597 0.031914           0.035683\n",
      "0.320000 0.069007 0.032594           0.036413\n",
      "0.330000 0.070348 0.033242           0.037106\n",
      "0.340000 0.071620 0.033858           0.037763\n",
      "0.350000 0.072822 0.034440           0.038381\n",
      "0.360000 0.073951 0.034990           0.038962\n",
      "0.370000 0.075008 0.035505           0.039503\n",
      "0.380000 0.075990 0.035985           0.040005\n",
      "0.390000 0.076898 0.036431           0.040467\n",
      "0.400000 0.077729 0.036840           0.040889\n",
      "0.410000 0.078484 0.037214           0.041271\n",
      "0.420000 0.079162 0.037551           0.041611\n",
      "0.430000 0.079761 0.037852           0.041910\n",
      "0.440000 0.080282 0.038115           0.042167\n",
      "0.450000 0.080723 0.038341           0.042383\n",
      "0.460000 0.081085 0.038529           0.042556\n",
      "0.470000 0.081367 0.038679           0.042688\n",
      "0.480000 0.081568 0.038791           0.042777\n",
      "0.490000 0.081689 0.038865           0.042824\n",
      "0.500000 0.081730 0.038901           0.042829\n",
      "0.510000 0.081689 0.038898           0.042791\n",
      "0.520000 0.081568 0.038857           0.042712\n",
      "0.530000 0.081367 0.038777           0.042590\n",
      "0.540000 0.081085 0.038659           0.042426\n",
      "0.550000 0.080723 0.038503           0.042220\n",
      "0.560000 0.080282 0.038309           0.041973\n",
      "0.570000 0.079761 0.038076           0.041685\n",
      "0.580000 0.079162 0.037806           0.041356\n",
      "0.590000 0.078484 0.037498           0.040986\n",
      "0.600000 0.077729 0.037153           0.040576\n",
      "0.610000 0.076898 0.036771           0.040127\n",
      "0.620000 0.075990 0.036353           0.039638\n",
      "0.630000 0.075008 0.035898           0.039110\n",
      "0.640000 0.073951 0.035407           0.038544\n",
      "0.650000 0.072822 0.034881           0.037941\n",
      "0.660000 0.071620 0.034320           0.037300\n",
      "0.670000 0.070348 0.033725           0.036624\n",
      "0.680000 0.069007 0.033095           0.035911\n",
      "0.690000 0.067597 0.032433           0.035164\n",
      "0.700000 0.066121 0.031738           0.034382\n",
      "0.710000 0.064579 0.031011           0.033568\n",
      "0.720000 0.062974 0.030253           0.032720\n",
      "0.730000 0.061306 0.029465           0.031842\n",
      "0.740000 0.059578 0.028646           0.030932\n",
      "0.750000 0.057792 0.027799           0.029992\n",
      "0.760000 0.055948 0.026924           0.029024\n",
      "0.770000 0.054049 0.026021           0.028028\n",
      "0.780000 0.052096 0.025092           0.027005\n",
      "0.790000 0.050093 0.024137           0.025956\n",
      "0.800000 0.048039 0.023158           0.024882\n",
      "0.810000 0.045939 0.022154           0.023784\n",
      "0.820000 0.043793 0.021129           0.022664\n",
      "0.830000 0.041604 0.020081           0.021523\n",
      "0.840000 0.039374 0.019013           0.020361\n",
      "0.850000 0.037104 0.017925           0.019180\n",
      "0.860000 0.034799 0.016818           0.017981\n",
      "0.870000 0.032459 0.015694           0.016765\n",
      "0.880000 0.030087 0.014553           0.015533\n",
      "0.890000 0.027685 0.013397           0.014287\n",
      "0.900000 0.025256 0.012227           0.013029\n",
      "0.910000 0.022802 0.011044           0.011758\n",
      "0.920000 0.020325 0.009849           0.010477\n",
      "0.930000 0.017829 0.008643           0.009186\n",
      "0.940000 0.015315 0.007427           0.007887\n",
      "0.950000 0.012785 0.006203           0.006582\n",
      "0.960000 0.010243 0.004972           0.005271\n",
      "0.970000 0.007691 0.003735           0.003956\n",
      "0.980000 0.005132 0.002493           0.002639\n",
      "0.990000 0.002567 0.001248           0.001319\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.04\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.003427 0.001601           0.001826\n",
      "0.020000 0.006850 0.003201           0.003649\n",
      "0.030000 0.010267 0.004800           0.005467\n",
      "0.040000 0.013674 0.006395           0.007278\n",
      "0.050000 0.017067 0.007986           0.009081\n",
      "0.060000 0.020443 0.009570           0.010873\n",
      "0.070000 0.023799 0.011146           0.012653\n",
      "0.080000 0.027132 0.012713           0.014419\n",
      "0.090000 0.030437 0.014268           0.016169\n",
      "0.100000 0.033713 0.015811           0.017902\n",
      "0.110000 0.036956 0.017340           0.019616\n",
      "0.120000 0.040162 0.018852           0.021309\n",
      "0.130000 0.043328 0.020348           0.022980\n",
      "0.140000 0.046452 0.021825           0.024627\n",
      "0.150000 0.049530 0.023281           0.026248\n",
      "0.160000 0.052558 0.024716           0.027843\n",
      "0.170000 0.055536 0.026128           0.029408\n",
      "0.180000 0.058458 0.027515           0.030943\n",
      "0.190000 0.061322 0.028876           0.032447\n",
      "0.200000 0.064126 0.030209           0.033917\n",
      "0.210000 0.066867 0.031514           0.035353\n",
      "0.220000 0.069542 0.032789           0.036752\n",
      "0.230000 0.072148 0.034033           0.038115\n",
      "0.240000 0.074683 0.035244           0.039438\n",
      "0.250000 0.077144 0.036422           0.040722\n",
      "0.260000 0.079529 0.037564           0.041965\n",
      "0.270000 0.081836 0.038671           0.043165\n",
      "0.280000 0.084062 0.039740           0.044322\n",
      "0.290000 0.086205 0.040770           0.045434\n",
      "0.300000 0.088262 0.041762           0.046501\n",
      "0.310000 0.090233 0.042712           0.047521\n",
      "0.320000 0.092115 0.043622           0.048493\n",
      "0.330000 0.093905 0.044489           0.049416\n",
      "0.340000 0.095604 0.045313           0.050290\n",
      "0.350000 0.097207 0.046093           0.051114\n",
      "0.360000 0.098715 0.046828           0.051887\n",
      "0.370000 0.100125 0.047517           0.052608\n",
      "0.380000 0.101437 0.048160           0.053277\n",
      "0.390000 0.102648 0.048756           0.053892\n",
      "0.400000 0.103759 0.049304           0.054454\n",
      "0.410000 0.104766 0.049804           0.054962\n",
      "0.420000 0.105671 0.050256           0.055415\n",
      "0.430000 0.106471 0.050657           0.055813\n",
      "0.440000 0.107166 0.051010           0.056156\n",
      "0.450000 0.107755 0.051312           0.056443\n",
      "0.460000 0.108238 0.051564           0.056674\n",
      "0.470000 0.108614 0.051765           0.056849\n",
      "0.480000 0.108883 0.051915           0.056968\n",
      "0.490000 0.109044 0.052013           0.057031\n",
      "0.500000 0.109098 0.052061           0.057037\n",
      "0.510000 0.109044 0.052057           0.056987\n",
      "0.520000 0.108883 0.052002           0.056881\n",
      "0.530000 0.108614 0.051895           0.056719\n",
      "0.540000 0.108238 0.051737           0.056501\n",
      "0.550000 0.107755 0.051528           0.056227\n",
      "0.560000 0.107166 0.051268           0.055898\n",
      "0.570000 0.106471 0.050957           0.055514\n",
      "0.580000 0.105671 0.050595           0.055075\n",
      "0.590000 0.104766 0.050183           0.054583\n",
      "0.600000 0.103759 0.049721           0.054037\n",
      "0.610000 0.102648 0.049210           0.053438\n",
      "0.620000 0.101437 0.048650           0.052787\n",
      "0.630000 0.100125 0.048041           0.052084\n",
      "0.640000 0.098715 0.047384           0.051331\n",
      "0.650000 0.097207 0.046680           0.050527\n",
      "0.660000 0.095604 0.045929           0.049674\n",
      "0.670000 0.093905 0.045132           0.048773\n",
      "0.680000 0.092115 0.044290           0.047824\n",
      "0.690000 0.090233 0.043404           0.046829\n",
      "0.700000 0.088262 0.042474           0.045788\n",
      "0.710000 0.086205 0.041501           0.044703\n",
      "0.720000 0.084062 0.040487           0.043575\n",
      "0.730000 0.081836 0.039431           0.042404\n",
      "0.740000 0.079529 0.038336           0.041193\n",
      "0.750000 0.077144 0.037202           0.039942\n",
      "0.760000 0.074683 0.036031           0.038652\n",
      "0.770000 0.072148 0.034822           0.037326\n",
      "0.780000 0.069542 0.033579           0.035963\n",
      "0.790000 0.066867 0.032301           0.034566\n",
      "0.800000 0.064126 0.030990           0.033136\n",
      "0.810000 0.061322 0.029648           0.031674\n",
      "0.820000 0.058458 0.028275           0.030183\n",
      "0.830000 0.055536 0.026873           0.028662\n",
      "0.840000 0.052558 0.025443           0.027115\n",
      "0.850000 0.049530 0.023987           0.025542\n",
      "0.860000 0.046452 0.022506           0.023945\n",
      "0.870000 0.043328 0.021002           0.022326\n",
      "0.880000 0.040162 0.019476           0.020686\n",
      "0.890000 0.036956 0.017929           0.019027\n",
      "0.900000 0.033713 0.016363           0.017351\n",
      "0.910000 0.030437 0.014779           0.015658\n",
      "0.920000 0.027132 0.013180           0.013952\n",
      "0.930000 0.023799 0.011566           0.012233\n",
      "0.940000 0.020443 0.009939           0.010504\n",
      "0.950000 0.017067 0.008301           0.008765\n",
      "0.960000 0.013674 0.006654           0.007020\n",
      "0.970000 0.010267 0.004998           0.005269\n",
      "0.980000 0.006850 0.003336           0.003514\n",
      "0.990000 0.003427 0.001670           0.001757\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.05\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.004290 0.002010           0.002280\n",
      "0.020000 0.008576 0.004020           0.004555\n",
      "0.030000 0.012853 0.006028           0.006825\n",
      "0.040000 0.017117 0.008032           0.009085\n",
      "0.050000 0.021365 0.010030           0.011335\n",
      "0.060000 0.025592 0.012019           0.013572\n",
      "0.070000 0.029793 0.013999           0.015794\n",
      "0.080000 0.033965 0.015966           0.017998\n",
      "0.090000 0.038103 0.017920           0.020183\n",
      "0.100000 0.042204 0.019857           0.022346\n",
      "0.110000 0.046263 0.021777           0.024486\n",
      "0.120000 0.050276 0.023677           0.026599\n",
      "0.130000 0.054240 0.025555           0.028685\n",
      "0.140000 0.058151 0.027410           0.030741\n",
      "0.150000 0.062004 0.029239           0.032765\n",
      "0.160000 0.065795 0.031041           0.034754\n",
      "0.170000 0.069522 0.032814           0.036709\n",
      "0.180000 0.073180 0.034556           0.038625\n",
      "0.190000 0.076766 0.036265           0.040501\n",
      "0.200000 0.080277 0.037940           0.042337\n",
      "0.210000 0.083708 0.039579           0.044129\n",
      "0.220000 0.087056 0.041180           0.045876\n",
      "0.230000 0.090318 0.042742           0.047577\n",
      "0.240000 0.093492 0.044263           0.049229\n",
      "0.250000 0.096573 0.045741           0.050831\n",
      "0.260000 0.099559 0.047176           0.052383\n",
      "0.270000 0.102446 0.048565           0.053881\n",
      "0.280000 0.105233 0.049908           0.055325\n",
      "0.290000 0.107915 0.051202           0.056713\n",
      "0.300000 0.110491 0.052447           0.058044\n",
      "0.310000 0.112958 0.053641           0.059317\n",
      "0.320000 0.115314 0.054783           0.060531\n",
      "0.330000 0.117555 0.055872           0.061684\n",
      "0.340000 0.119681 0.056907           0.062775\n",
      "0.350000 0.121689 0.057886           0.063803\n",
      "0.360000 0.123576 0.058809           0.064768\n",
      "0.370000 0.125342 0.059674           0.065668\n",
      "0.380000 0.126984 0.060482           0.066502\n",
      "0.390000 0.128500 0.061230           0.067271\n",
      "0.400000 0.129890 0.061918           0.067972\n",
      "0.410000 0.131152 0.062546           0.068606\n",
      "0.420000 0.132284 0.063113           0.069171\n",
      "0.430000 0.133285 0.063617           0.069668\n",
      "0.440000 0.134155 0.064059           0.070096\n",
      "0.450000 0.134893 0.064439           0.070454\n",
      "0.460000 0.135498 0.064755           0.070743\n",
      "0.470000 0.135968 0.065007           0.070961\n",
      "0.480000 0.136305 0.065195           0.071110\n",
      "0.490000 0.136507 0.065319           0.071188\n",
      "0.500000 0.136575 0.065379           0.071196\n",
      "0.510000 0.136507 0.065374           0.071133\n",
      "0.520000 0.136305 0.065304           0.071001\n",
      "0.530000 0.135968 0.065170           0.070798\n",
      "0.540000 0.135498 0.064972           0.070526\n",
      "0.550000 0.134893 0.064709           0.070184\n",
      "0.560000 0.134155 0.064382           0.069773\n",
      "0.570000 0.133285 0.063991           0.069294\n",
      "0.580000 0.132284 0.063537           0.068747\n",
      "0.590000 0.131152 0.063020           0.068132\n",
      "0.600000 0.129890 0.062439           0.067451\n",
      "0.610000 0.128500 0.061797           0.066703\n",
      "0.620000 0.126984 0.061093           0.065890\n",
      "0.630000 0.125342 0.060329           0.065013\n",
      "0.640000 0.123576 0.059504           0.064073\n",
      "0.650000 0.121689 0.058619           0.063069\n",
      "0.660000 0.119681 0.057677           0.062005\n",
      "0.670000 0.117555 0.056676           0.060880\n",
      "0.680000 0.115314 0.055618           0.059695\n",
      "0.690000 0.112958 0.054505           0.058453\n",
      "0.700000 0.110491 0.053337           0.057154\n",
      "0.710000 0.107915 0.052115           0.055800\n",
      "0.720000 0.105233 0.050841           0.054391\n",
      "0.730000 0.102446 0.049516           0.052930\n",
      "0.740000 0.099559 0.048141           0.051418\n",
      "0.750000 0.096573 0.046717           0.049856\n",
      "0.760000 0.093492 0.045245           0.048247\n",
      "0.770000 0.090318 0.043728           0.046590\n",
      "0.780000 0.087056 0.042166           0.044890\n",
      "0.790000 0.083708 0.040562           0.043146\n",
      "0.800000 0.080277 0.038916           0.041361\n",
      "0.810000 0.076766 0.037230           0.039537\n",
      "0.820000 0.073180 0.035506           0.037675\n",
      "0.830000 0.069522 0.033745           0.035777\n",
      "0.840000 0.065795 0.031950           0.033845\n",
      "0.850000 0.062004 0.030121           0.031882\n",
      "0.860000 0.058151 0.028262           0.029889\n",
      "0.870000 0.054240 0.026373           0.027868\n",
      "0.880000 0.050276 0.024456           0.025821\n",
      "0.890000 0.046263 0.022513           0.023750\n",
      "0.900000 0.042204 0.020547           0.021657\n",
      "0.910000 0.038103 0.018558           0.019545\n",
      "0.920000 0.033965 0.016550           0.017415\n",
      "0.930000 0.029793 0.014523           0.015270\n",
      "0.940000 0.025592 0.012481           0.013111\n",
      "0.950000 0.021365 0.010424           0.010941\n",
      "0.960000 0.017117 0.008355           0.008762\n",
      "0.970000 0.012853 0.006276           0.006577\n",
      "0.980000 0.008576 0.004189           0.004386\n",
      "0.990000 0.004290 0.002097           0.002193\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.06\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.005157 0.002426           0.002731\n",
      "0.020000 0.010309 0.004852           0.005458\n",
      "0.030000 0.015451 0.007275           0.008176\n",
      "0.040000 0.020578 0.009693           0.010885\n",
      "0.050000 0.025684 0.012104           0.013580\n",
      "0.060000 0.030765 0.014505           0.016260\n",
      "0.070000 0.035816 0.016894           0.018922\n",
      "0.080000 0.040831 0.019268           0.021563\n",
      "0.090000 0.045806 0.021626           0.024181\n",
      "0.100000 0.050736 0.023964           0.026772\n",
      "0.110000 0.055616 0.026280           0.029335\n",
      "0.120000 0.060441 0.028573           0.031868\n",
      "0.130000 0.065206 0.030840           0.034366\n",
      "0.140000 0.069907 0.033078           0.036829\n",
      "0.150000 0.074539 0.035285           0.039254\n",
      "0.160000 0.079097 0.037459           0.041638\n",
      "0.170000 0.083577 0.039599           0.043979\n",
      "0.180000 0.087975 0.041701           0.046275\n",
      "0.190000 0.092286 0.043763           0.048523\n",
      "0.200000 0.096506 0.045784           0.050722\n",
      "0.210000 0.100631 0.047762           0.052869\n",
      "0.220000 0.104656 0.049694           0.054962\n",
      "0.230000 0.108578 0.051579           0.056999\n",
      "0.240000 0.112393 0.053414           0.058979\n",
      "0.250000 0.116097 0.055198           0.060898\n",
      "0.260000 0.119686 0.056929           0.062757\n",
      "0.270000 0.123158 0.058606           0.064552\n",
      "0.280000 0.126507 0.060226           0.066282\n",
      "0.290000 0.129732 0.061787           0.067945\n",
      "0.300000 0.132829 0.063289           0.069540\n",
      "0.310000 0.135795 0.064730           0.071065\n",
      "0.320000 0.138627 0.066108           0.072518\n",
      "0.330000 0.141322 0.067422           0.073900\n",
      "0.340000 0.143877 0.068670           0.075207\n",
      "0.350000 0.146291 0.069852           0.076439\n",
      "0.360000 0.148560 0.070965           0.077594\n",
      "0.370000 0.150682 0.072010           0.078673\n",
      "0.380000 0.152656 0.072984           0.079672\n",
      "0.390000 0.154479 0.073886           0.080593\n",
      "0.400000 0.156150 0.074717           0.081433\n",
      "0.410000 0.157666 0.075474           0.082192\n",
      "0.420000 0.159027 0.076158           0.082870\n",
      "0.430000 0.160232 0.076766           0.083465\n",
      "0.440000 0.161278 0.077300           0.083978\n",
      "0.450000 0.162164 0.077757           0.084407\n",
      "0.460000 0.162891 0.078138           0.084753\n",
      "0.470000 0.163457 0.078443           0.085014\n",
      "0.480000 0.163862 0.078670           0.085192\n",
      "0.490000 0.164105 0.078819           0.085286\n",
      "0.500000 0.164186 0.078891           0.085295\n",
      "0.510000 0.164105 0.078885           0.085220\n",
      "0.520000 0.163862 0.078801           0.085061\n",
      "0.530000 0.163457 0.078639           0.084818\n",
      "0.540000 0.162891 0.078399           0.084492\n",
      "0.550000 0.162164 0.078082           0.084083\n",
      "0.560000 0.161278 0.077687           0.083590\n",
      "0.570000 0.160232 0.077215           0.083016\n",
      "0.580000 0.159027 0.076667           0.082361\n",
      "0.590000 0.157666 0.076042           0.081624\n",
      "0.600000 0.156150 0.075342           0.080808\n",
      "0.610000 0.154479 0.074567           0.079912\n",
      "0.620000 0.152656 0.073718           0.078938\n",
      "0.630000 0.150682 0.072795           0.077887\n",
      "0.640000 0.148560 0.071799           0.076760\n",
      "0.650000 0.146291 0.070732           0.075559\n",
      "0.660000 0.143877 0.069594           0.074283\n",
      "0.670000 0.141322 0.068386           0.072935\n",
      "0.680000 0.138627 0.067110           0.071516\n",
      "0.690000 0.135795 0.065767           0.070028\n",
      "0.700000 0.132829 0.064357           0.068472\n",
      "0.710000 0.129732 0.062883           0.066849\n",
      "0.720000 0.126507 0.061346           0.065162\n",
      "0.730000 0.123158 0.059746           0.063411\n",
      "0.740000 0.119686 0.058086           0.061600\n",
      "0.750000 0.116097 0.056368           0.059729\n",
      "0.760000 0.112393 0.054593           0.057800\n",
      "0.770000 0.108578 0.052762           0.055816\n",
      "0.780000 0.104656 0.050877           0.053779\n",
      "0.790000 0.100631 0.048941           0.051690\n",
      "0.800000 0.096506 0.046955           0.049551\n",
      "0.810000 0.092286 0.044921           0.047365\n",
      "0.820000 0.087975 0.042840           0.045135\n",
      "0.830000 0.083577 0.040716           0.042861\n",
      "0.840000 0.079097 0.038550           0.040547\n",
      "0.850000 0.074539 0.036344           0.038195\n",
      "0.860000 0.069907 0.034100           0.035807\n",
      "0.870000 0.065206 0.031820           0.033386\n",
      "0.880000 0.060441 0.029507           0.030933\n",
      "0.890000 0.055616 0.027163           0.028453\n",
      "0.900000 0.050736 0.024791           0.025945\n",
      "0.910000 0.045806 0.022391           0.023415\n",
      "0.920000 0.040831 0.019968           0.020863\n",
      "0.930000 0.035816 0.017523           0.018293\n",
      "0.940000 0.030765 0.015058           0.015707\n",
      "0.950000 0.025684 0.012577           0.013107\n",
      "0.960000 0.020578 0.010081           0.010497\n",
      "0.970000 0.015451 0.007573           0.007879\n",
      "0.980000 0.010309 0.005055           0.005255\n",
      "0.990000 0.005157 0.002530           0.002628\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.07\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.006030 0.002849           0.003181\n",
      "0.020000 0.012053 0.005698           0.006356\n",
      "0.030000 0.018065 0.008543           0.009522\n",
      "0.040000 0.024059 0.011383           0.012676\n",
      "0.050000 0.030029 0.014214           0.015815\n",
      "0.060000 0.035970 0.017034           0.018936\n",
      "0.070000 0.041875 0.019839           0.022035\n",
      "0.080000 0.047738 0.022628           0.025111\n",
      "0.090000 0.053555 0.025396           0.028159\n",
      "0.100000 0.059319 0.028142           0.031177\n",
      "0.110000 0.065024 0.030862           0.034162\n",
      "0.120000 0.070665 0.033554           0.037110\n",
      "0.130000 0.076236 0.036216           0.040020\n",
      "0.140000 0.081732 0.038844           0.042888\n",
      "0.150000 0.087148 0.041436           0.045712\n",
      "0.160000 0.092477 0.043989           0.048488\n",
      "0.170000 0.097715 0.046501           0.051214\n",
      "0.180000 0.102857 0.048969           0.053887\n",
      "0.190000 0.107897 0.051391           0.056505\n",
      "0.200000 0.112831 0.053765           0.059066\n",
      "0.210000 0.117653 0.056087           0.061566\n",
      "0.220000 0.122359 0.058356           0.064003\n",
      "0.230000 0.126945 0.060569           0.066376\n",
      "0.240000 0.131405 0.062724           0.068681\n",
      "0.250000 0.135735 0.064819           0.070917\n",
      "0.260000 0.139932 0.066851           0.073081\n",
      "0.270000 0.143990 0.068820           0.075171\n",
      "0.280000 0.147907 0.070722           0.077185\n",
      "0.290000 0.151677 0.072555           0.079122\n",
      "0.300000 0.155298 0.074319           0.080979\n",
      "0.310000 0.158765 0.076011           0.082755\n",
      "0.320000 0.162076 0.077628           0.084448\n",
      "0.330000 0.165227 0.079171           0.086056\n",
      "0.340000 0.168215 0.080637           0.087578\n",
      "0.350000 0.171037 0.082024           0.089013\n",
      "0.360000 0.173690 0.083331           0.090359\n",
      "0.370000 0.176171 0.084557           0.091614\n",
      "0.380000 0.178479 0.085701           0.092778\n",
      "0.390000 0.180610 0.086760           0.093850\n",
      "0.400000 0.182564 0.087735           0.094828\n",
      "0.410000 0.184337 0.088624           0.095713\n",
      "0.420000 0.185928 0.089427           0.096502\n",
      "0.430000 0.187336 0.090141           0.097195\n",
      "0.440000 0.188559 0.090767           0.097791\n",
      "0.450000 0.189596 0.091304           0.098291\n",
      "0.460000 0.190445 0.091752           0.098694\n",
      "0.470000 0.191107 0.092108           0.098998\n",
      "0.480000 0.191580 0.092375           0.099205\n",
      "0.490000 0.191864 0.092550           0.099314\n",
      "0.500000 0.191959 0.092634           0.099325\n",
      "0.510000 0.191864 0.092627           0.099238\n",
      "0.520000 0.191580 0.092528           0.099052\n",
      "0.530000 0.191107 0.092337           0.098770\n",
      "0.540000 0.190445 0.092056           0.098390\n",
      "0.550000 0.189596 0.091683           0.097913\n",
      "0.560000 0.188559 0.091219           0.097340\n",
      "0.570000 0.187336 0.090665           0.096671\n",
      "0.580000 0.185928 0.090021           0.095908\n",
      "0.590000 0.184337 0.089287           0.095050\n",
      "0.600000 0.182564 0.088465           0.094099\n",
      "0.610000 0.180610 0.087554           0.093056\n",
      "0.620000 0.178479 0.086557           0.091922\n",
      "0.630000 0.176171 0.085473           0.090698\n",
      "0.640000 0.173690 0.084304           0.089386\n",
      "0.650000 0.171037 0.083050           0.087986\n",
      "0.660000 0.168215 0.081714           0.086501\n",
      "0.670000 0.165227 0.080296           0.084931\n",
      "0.680000 0.162076 0.078797           0.083279\n",
      "0.690000 0.158765 0.077219           0.081546\n",
      "0.700000 0.155298 0.075564           0.079734\n",
      "0.710000 0.151677 0.073833           0.077844\n",
      "0.720000 0.147907 0.072028           0.075879\n",
      "0.730000 0.143990 0.070150           0.073841\n",
      "0.740000 0.139932 0.068201           0.071731\n",
      "0.750000 0.135735 0.066183           0.069552\n",
      "0.760000 0.131405 0.064098           0.067307\n",
      "0.770000 0.126945 0.061948           0.064996\n",
      "0.780000 0.122359 0.059736           0.062624\n",
      "0.790000 0.117653 0.057462           0.060191\n",
      "0.800000 0.112831 0.055130           0.057701\n",
      "0.810000 0.107897 0.052741           0.055156\n",
      "0.820000 0.102857 0.050299           0.052558\n",
      "0.830000 0.097715 0.047804           0.049911\n",
      "0.840000 0.092477 0.045261           0.047216\n",
      "0.850000 0.087148 0.042671           0.044477\n",
      "0.860000 0.081732 0.040036           0.041696\n",
      "0.870000 0.076236 0.037359           0.038877\n",
      "0.880000 0.070665 0.034644           0.036021\n",
      "0.890000 0.065024 0.031892           0.033132\n",
      "0.900000 0.059319 0.029106           0.030213\n",
      "0.910000 0.053555 0.026289           0.027266\n",
      "0.920000 0.047738 0.023444           0.024294\n",
      "0.930000 0.041875 0.020573           0.021302\n",
      "0.940000 0.035970 0.017679           0.018290\n",
      "0.950000 0.030029 0.014766           0.015263\n",
      "0.960000 0.024059 0.011835           0.012224\n",
      "0.970000 0.018065 0.008891           0.009174\n",
      "0.980000 0.012053 0.005934           0.006119\n",
      "0.990000 0.006030 0.002970           0.003060\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.08\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.006908 0.003280           0.003628\n",
      "0.020000 0.013809 0.006560           0.007249\n",
      "0.030000 0.020696 0.009837           0.010859\n",
      "0.040000 0.027563 0.013107           0.014457\n",
      "0.050000 0.034403 0.016367           0.018037\n",
      "0.060000 0.041209 0.019613           0.021596\n",
      "0.070000 0.047974 0.022843           0.025131\n",
      "0.080000 0.054692 0.026054           0.028639\n",
      "0.090000 0.061356 0.029241           0.032115\n",
      "0.100000 0.067959 0.032402           0.035557\n",
      "0.110000 0.074496 0.035535           0.038961\n",
      "0.120000 0.080959 0.038634           0.042324\n",
      "0.130000 0.087341 0.041699           0.045643\n",
      "0.140000 0.093638 0.044724           0.048914\n",
      "0.150000 0.099842 0.047709           0.052134\n",
      "0.160000 0.105948 0.050648           0.055300\n",
      "0.170000 0.111949 0.053540           0.058409\n",
      "0.180000 0.117840 0.056382           0.061458\n",
      "0.190000 0.123614 0.059171           0.064444\n",
      "0.200000 0.129267 0.061903           0.067364\n",
      "0.210000 0.134791 0.064576           0.070215\n",
      "0.220000 0.140183 0.067188           0.072995\n",
      "0.230000 0.145437 0.069736           0.075701\n",
      "0.240000 0.150547 0.072217           0.078330\n",
      "0.250000 0.155508 0.074629           0.080879\n",
      "0.260000 0.160316 0.076969           0.083347\n",
      "0.270000 0.164966 0.079235           0.085731\n",
      "0.280000 0.169452 0.081424           0.088028\n",
      "0.290000 0.173772 0.083535           0.090237\n",
      "0.300000 0.177920 0.085565           0.092355\n",
      "0.310000 0.181893 0.087513           0.094380\n",
      "0.320000 0.185686 0.089375           0.096311\n",
      "0.330000 0.189296 0.091151           0.098145\n",
      "0.340000 0.192719 0.092838           0.099881\n",
      "0.350000 0.195952 0.094435           0.101517\n",
      "0.360000 0.198991 0.095939           0.103052\n",
      "0.370000 0.201834 0.097351           0.104483\n",
      "0.380000 0.204478 0.098667           0.105811\n",
      "0.390000 0.206920 0.099887           0.107033\n",
      "0.400000 0.209158 0.101009           0.108149\n",
      "0.410000 0.211189 0.102032           0.109157\n",
      "0.420000 0.213012 0.102955           0.110057\n",
      "0.430000 0.214625 0.103778           0.110847\n",
      "0.440000 0.216026 0.104498           0.111528\n",
      "0.450000 0.217214 0.105116           0.112098\n",
      "0.460000 0.218187 0.105631           0.112557\n",
      "0.470000 0.218946 0.106041           0.112904\n",
      "0.480000 0.219488 0.106347           0.113140\n",
      "0.490000 0.219813 0.106549           0.113264\n",
      "0.500000 0.219922 0.106645           0.113276\n",
      "0.510000 0.219813 0.106636           0.113177\n",
      "0.520000 0.219488 0.106522           0.112965\n",
      "0.530000 0.218946 0.106303           0.112643\n",
      "0.540000 0.218187 0.105978           0.112210\n",
      "0.550000 0.217214 0.105548           0.111666\n",
      "0.560000 0.216026 0.105014           0.111012\n",
      "0.570000 0.214625 0.104376           0.110249\n",
      "0.580000 0.213012 0.103634           0.109378\n",
      "0.590000 0.211189 0.102789           0.108400\n",
      "0.600000 0.209158 0.101842           0.107316\n",
      "0.610000 0.206920 0.100794           0.106126\n",
      "0.620000 0.204478 0.099645           0.104833\n",
      "0.630000 0.201834 0.098397           0.103437\n",
      "0.640000 0.198991 0.097050           0.101941\n",
      "0.650000 0.195952 0.095607           0.100344\n",
      "0.660000 0.192719 0.094069           0.098650\n",
      "0.670000 0.189296 0.092436           0.096860\n",
      "0.680000 0.185686 0.090710           0.094976\n",
      "0.690000 0.181893 0.088894           0.092999\n",
      "0.700000 0.177920 0.086988           0.090932\n",
      "0.710000 0.173772 0.084995           0.088777\n",
      "0.720000 0.169452 0.082916           0.086536\n",
      "0.730000 0.164966 0.080754           0.084211\n",
      "0.740000 0.160316 0.078510           0.081806\n",
      "0.750000 0.155508 0.076187           0.079321\n",
      "0.760000 0.150547 0.073787           0.076760\n",
      "0.770000 0.145437 0.071312           0.074125\n",
      "0.780000 0.140183 0.068765           0.071419\n",
      "0.790000 0.134791 0.066147           0.068644\n",
      "0.800000 0.129267 0.063462           0.065804\n",
      "0.810000 0.123614 0.060713           0.062902\n",
      "0.820000 0.117840 0.057901           0.059939\n",
      "0.830000 0.111949 0.055029           0.056920\n",
      "0.840000 0.105948 0.052101           0.053847\n",
      "0.850000 0.099842 0.049119           0.050723\n",
      "0.860000 0.093638 0.046086           0.047552\n",
      "0.870000 0.087341 0.043005           0.044336\n",
      "0.880000 0.080959 0.039879           0.041079\n",
      "0.890000 0.074496 0.036711           0.037785\n",
      "0.900000 0.067959 0.033504           0.034455\n",
      "0.910000 0.061356 0.030261           0.031095\n",
      "0.920000 0.054692 0.026986           0.027706\n",
      "0.930000 0.047974 0.023681           0.024293\n",
      "0.940000 0.041209 0.020351           0.020859\n",
      "0.950000 0.034403 0.016997           0.017407\n",
      "0.960000 0.027563 0.013623           0.013940\n",
      "0.970000 0.020696 0.010234           0.010463\n",
      "0.980000 0.013809 0.006831           0.006978\n",
      "0.990000 0.006908 0.003419           0.003489\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.09\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.007793 0.003721           0.004072\n",
      "0.020000 0.015578 0.007442           0.008136\n",
      "0.030000 0.023348 0.011160           0.012189\n",
      "0.040000 0.031095 0.014869           0.016226\n",
      "0.050000 0.038812 0.018567           0.020245\n",
      "0.060000 0.046490 0.022250           0.024240\n",
      "0.070000 0.054122 0.025914           0.028208\n",
      "0.080000 0.061700 0.029556           0.032145\n",
      "0.090000 0.069218 0.033172           0.036046\n",
      "0.100000 0.076668 0.036758           0.039910\n",
      "0.110000 0.084041 0.040311           0.043731\n",
      "0.120000 0.091332 0.043827           0.047505\n",
      "0.130000 0.098533 0.047303           0.051230\n",
      "0.140000 0.105636 0.050735           0.054901\n",
      "0.150000 0.112636 0.054120           0.058515\n",
      "0.160000 0.119524 0.057455           0.062069\n",
      "0.170000 0.126294 0.060735           0.065559\n",
      "0.180000 0.132939 0.063959           0.068981\n",
      "0.190000 0.139454 0.067121           0.072332\n",
      "0.200000 0.145830 0.070221           0.075610\n",
      "0.210000 0.152063 0.073253           0.078810\n",
      "0.220000 0.158146 0.076216           0.081930\n",
      "0.230000 0.164072 0.079105           0.084967\n",
      "0.240000 0.169837 0.081920           0.087917\n",
      "0.250000 0.175434 0.084655           0.090779\n",
      "0.260000 0.180858 0.087309           0.093549\n",
      "0.270000 0.186104 0.089879           0.096224\n",
      "0.280000 0.191165 0.092362           0.098803\n",
      "0.290000 0.196038 0.094757           0.101282\n",
      "0.300000 0.200718 0.097059           0.103659\n",
      "0.310000 0.205200 0.099268           0.105932\n",
      "0.320000 0.209479 0.101380           0.108099\n",
      "0.330000 0.213551 0.103394           0.110158\n",
      "0.340000 0.217413 0.105307           0.112106\n",
      "0.350000 0.221060 0.107118           0.113942\n",
      "0.360000 0.224489 0.108824           0.115665\n",
      "0.370000 0.227696 0.110425           0.117272\n",
      "0.380000 0.230679 0.111917           0.118762\n",
      "0.390000 0.233434 0.113300           0.120133\n",
      "0.400000 0.235958 0.114573           0.121386\n",
      "0.410000 0.238250 0.115733           0.122517\n",
      "0.420000 0.240307 0.116780           0.123527\n",
      "0.430000 0.242126 0.117712           0.124414\n",
      "0.440000 0.243707 0.118529           0.125178\n",
      "0.450000 0.245047 0.119229           0.125817\n",
      "0.460000 0.246145 0.119813           0.126332\n",
      "0.470000 0.247000 0.120278           0.126722\n",
      "0.480000 0.247612 0.120625           0.126987\n",
      "0.490000 0.247979 0.120853           0.127126\n",
      "0.500000 0.248101 0.120962           0.127139\n",
      "0.510000 0.247979 0.120951           0.127028\n",
      "0.520000 0.247612 0.120821           0.126790\n",
      "0.530000 0.247000 0.120572           0.126428\n",
      "0.540000 0.246145 0.120203           0.125942\n",
      "0.550000 0.245047 0.119716           0.125331\n",
      "0.560000 0.243707 0.119109           0.124598\n",
      "0.570000 0.242126 0.118385           0.123741\n",
      "0.580000 0.240307 0.117543           0.122764\n",
      "0.590000 0.238250 0.116584           0.121666\n",
      "0.600000 0.235958 0.115510           0.120449\n",
      "0.610000 0.233434 0.114320           0.119114\n",
      "0.620000 0.230679 0.113017           0.117662\n",
      "0.630000 0.227696 0.111601           0.116095\n",
      "0.640000 0.224489 0.110074           0.114415\n",
      "0.650000 0.221060 0.108436           0.112623\n",
      "0.660000 0.217413 0.106691           0.110722\n",
      "0.670000 0.213551 0.104838           0.108713\n",
      "0.680000 0.209479 0.102881           0.106598\n",
      "0.690000 0.205200 0.100821           0.104379\n",
      "0.700000 0.200718 0.098659           0.102059\n",
      "0.710000 0.196038 0.096398           0.099640\n",
      "0.720000 0.191165 0.094040           0.097125\n",
      "0.730000 0.186104 0.091588           0.094516\n",
      "0.740000 0.180858 0.089043           0.091816\n",
      "0.750000 0.175434 0.086408           0.089027\n",
      "0.760000 0.169837 0.083685           0.086152\n",
      "0.770000 0.164072 0.080878           0.083195\n",
      "0.780000 0.158146 0.077988           0.080157\n",
      "0.790000 0.152063 0.075020           0.077043\n",
      "0.800000 0.145830 0.071974           0.073856\n",
      "0.810000 0.139454 0.068856           0.070598\n",
      "0.820000 0.132939 0.065666           0.067273\n",
      "0.830000 0.126294 0.062409           0.063884\n",
      "0.840000 0.119524 0.059088           0.060435\n",
      "0.850000 0.112636 0.055706           0.056929\n",
      "0.860000 0.105636 0.052266           0.053370\n",
      "0.870000 0.098533 0.048772           0.049761\n",
      "0.880000 0.091332 0.045227           0.046106\n",
      "0.890000 0.084041 0.041634           0.042408\n",
      "0.900000 0.076668 0.037997           0.038671\n",
      "0.910000 0.069218 0.034319           0.034899\n",
      "0.920000 0.061700 0.030604           0.031096\n",
      "0.930000 0.054122 0.026856           0.027265\n",
      "0.940000 0.046490 0.023079           0.023411\n",
      "0.950000 0.038812 0.019275           0.019536\n",
      "0.960000 0.031095 0.015450           0.015646\n",
      "0.970000 0.023348 0.011606           0.011743\n",
      "0.980000 0.015578 0.007747           0.007832\n",
      "0.990000 0.007793 0.003877           0.003916\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.1\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.008686 0.004173           0.004513\n",
      "0.020000 0.017363 0.008346           0.009017\n",
      "0.030000 0.026023 0.012514           0.013509\n",
      "0.040000 0.034658 0.016674           0.017984\n",
      "0.050000 0.043258 0.020821           0.022437\n",
      "0.060000 0.051816 0.024951           0.026865\n",
      "0.070000 0.060322 0.029060           0.031263\n",
      "0.080000 0.068769 0.033143           0.035626\n",
      "0.090000 0.077148 0.037198           0.039950\n",
      "0.100000 0.085451 0.041219           0.044232\n",
      "0.110000 0.093670 0.045203           0.048467\n",
      "0.120000 0.101796 0.049146           0.052650\n",
      "0.130000 0.109822 0.053043           0.056778\n",
      "0.140000 0.117739 0.056892           0.060847\n",
      "0.150000 0.125540 0.060688           0.064853\n",
      "0.160000 0.133217 0.064426           0.068791\n",
      "0.170000 0.140763 0.068105           0.072658\n",
      "0.180000 0.148170 0.071719           0.076451\n",
      "0.190000 0.155431 0.075265           0.080165\n",
      "0.200000 0.162538 0.078740           0.083798\n",
      "0.210000 0.169485 0.082140           0.087345\n",
      "0.220000 0.176264 0.085462           0.090802\n",
      "0.230000 0.182870 0.088702           0.094168\n",
      "0.240000 0.189295 0.091857           0.097438\n",
      "0.250000 0.195533 0.094924           0.100610\n",
      "0.260000 0.201579 0.097899           0.103679\n",
      "0.270000 0.207425 0.100781           0.106644\n",
      "0.280000 0.213067 0.103565           0.109502\n",
      "0.290000 0.218498 0.106249           0.112249\n",
      "0.300000 0.223714 0.108830           0.114884\n",
      "0.310000 0.228709 0.111306           0.117403\n",
      "0.320000 0.233479 0.113674           0.119804\n",
      "0.330000 0.238017 0.115932           0.122086\n",
      "0.340000 0.242321 0.118077           0.124245\n",
      "0.350000 0.246386 0.120107           0.126280\n",
      "0.360000 0.250208 0.122019           0.128189\n",
      "0.370000 0.253783 0.123813           0.129970\n",
      "0.380000 0.257107 0.125486           0.131621\n",
      "0.390000 0.260178 0.127037           0.133141\n",
      "0.400000 0.262992 0.128463           0.134529\n",
      "0.410000 0.265546 0.129763           0.135783\n",
      "0.420000 0.267838 0.130937           0.136902\n",
      "0.430000 0.269866 0.131982           0.137885\n",
      "0.440000 0.271628 0.132897           0.138731\n",
      "0.450000 0.273121 0.133682           0.139440\n",
      "0.460000 0.274345 0.134335           0.140010\n",
      "0.470000 0.275299 0.134856           0.140442\n",
      "0.480000 0.275980 0.135245           0.140735\n",
      "0.490000 0.276389 0.135500           0.140890\n",
      "0.500000 0.276526 0.135621           0.140904\n",
      "0.510000 0.276389 0.135609           0.140780\n",
      "0.520000 0.275980 0.135463           0.140517\n",
      "0.530000 0.275299 0.135183           0.140116\n",
      "0.540000 0.274345 0.134769           0.139577\n",
      "0.550000 0.273121 0.134221           0.138900\n",
      "0.560000 0.271628 0.133541           0.138087\n",
      "0.570000 0.269866 0.132728           0.137138\n",
      "0.580000 0.267838 0.131784           0.136054\n",
      "0.590000 0.265546 0.130709           0.134837\n",
      "0.600000 0.262992 0.129504           0.133488\n",
      "0.610000 0.260178 0.128169           0.132008\n",
      "0.620000 0.257107 0.126708           0.130400\n",
      "0.630000 0.253783 0.125120           0.128663\n",
      "0.640000 0.250208 0.123407           0.126801\n",
      "0.650000 0.246386 0.121571           0.124815\n",
      "0.660000 0.242321 0.119613           0.122708\n",
      "0.670000 0.238017 0.117536           0.120481\n",
      "0.680000 0.233479 0.115341           0.118137\n",
      "0.690000 0.228709 0.113031           0.115678\n",
      "0.700000 0.223714 0.110607           0.113107\n",
      "0.710000 0.218498 0.108072           0.110426\n",
      "0.720000 0.213067 0.105428           0.107639\n",
      "0.730000 0.207425 0.102678           0.104747\n",
      "0.740000 0.201579 0.099825           0.101754\n",
      "0.750000 0.195533 0.096870           0.098663\n",
      "0.760000 0.189295 0.093818           0.095477\n",
      "0.770000 0.182870 0.090670           0.092200\n",
      "0.780000 0.176264 0.087430           0.088834\n",
      "0.790000 0.169485 0.084102           0.085383\n",
      "0.800000 0.162538 0.080688           0.081850\n",
      "0.810000 0.155431 0.077191           0.078240\n",
      "0.820000 0.148170 0.073615           0.074555\n",
      "0.830000 0.140763 0.069964           0.070799\n",
      "0.840000 0.133217 0.066241           0.066977\n",
      "0.850000 0.125540 0.062449           0.063091\n",
      "0.860000 0.117739 0.058592           0.059147\n",
      "0.870000 0.109822 0.054675           0.055147\n",
      "0.880000 0.101796 0.050700           0.051096\n",
      "0.890000 0.093670 0.046672           0.046998\n",
      "0.900000 0.085451 0.042595           0.042856\n",
      "0.910000 0.077148 0.038472           0.038676\n",
      "0.920000 0.068769 0.034308           0.034461\n",
      "0.930000 0.060322 0.030106           0.030216\n",
      "0.940000 0.051816 0.025871           0.025944\n",
      "0.950000 0.043258 0.021608           0.021650\n",
      "0.960000 0.034658 0.017319           0.017339\n",
      "0.970000 0.026023 0.013010           0.013014\n",
      "0.980000 0.017363 0.008684           0.008679\n",
      "0.990000 0.008686 0.004346           0.004340\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.11\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.009587 0.004637           0.004950\n",
      "0.020000 0.019165 0.009274           0.009892\n",
      "0.030000 0.028724 0.013905           0.014819\n",
      "0.040000 0.038255 0.018527           0.019728\n",
      "0.050000 0.047747 0.023134           0.024613\n",
      "0.060000 0.057193 0.027723           0.029470\n",
      "0.070000 0.066582 0.032288           0.034294\n",
      "0.080000 0.075906 0.036826           0.039080\n",
      "0.090000 0.085155 0.041330           0.043824\n",
      "0.100000 0.094319 0.045798           0.048521\n",
      "0.110000 0.103391 0.050225           0.053166\n",
      "0.120000 0.112360 0.054605           0.057755\n",
      "0.130000 0.121219 0.058935           0.062283\n",
      "0.140000 0.129958 0.063211           0.066747\n",
      "0.150000 0.138569 0.067428           0.071141\n",
      "0.160000 0.147043 0.071582           0.075461\n",
      "0.170000 0.155371 0.075668           0.079703\n",
      "0.180000 0.163547 0.079683           0.083863\n",
      "0.190000 0.171561 0.083623           0.087938\n",
      "0.200000 0.179406 0.087484           0.091922\n",
      "0.210000 0.187074 0.091261           0.095813\n",
      "0.220000 0.194557 0.094951           0.099606\n",
      "0.230000 0.201848 0.098550           0.103298\n",
      "0.240000 0.208940 0.102055           0.106885\n",
      "0.250000 0.215826 0.105462           0.110364\n",
      "0.260000 0.222498 0.108768           0.113731\n",
      "0.270000 0.228951 0.111968           0.116983\n",
      "0.280000 0.235179 0.115061           0.120118\n",
      "0.290000 0.241174 0.118043           0.123131\n",
      "0.300000 0.246931 0.120910           0.126021\n",
      "0.310000 0.252444 0.123660           0.128784\n",
      "0.320000 0.257709 0.126290           0.131418\n",
      "0.330000 0.262719 0.128798           0.133921\n",
      "0.340000 0.267469 0.131180           0.136289\n",
      "0.350000 0.271956 0.133435           0.138521\n",
      "0.360000 0.276174 0.135559           0.140615\n",
      "0.370000 0.280120 0.137552           0.142568\n",
      "0.380000 0.283790 0.139410           0.144380\n",
      "0.390000 0.287179 0.141132           0.146047\n",
      "0.400000 0.290285 0.142716           0.147569\n",
      "0.410000 0.293104 0.144160           0.148944\n",
      "0.420000 0.295634 0.145462           0.150172\n",
      "0.430000 0.297873 0.146623           0.151250\n",
      "0.440000 0.299817 0.147639           0.152178\n",
      "0.450000 0.301466 0.148510           0.152955\n",
      "0.460000 0.302817 0.149235           0.153581\n",
      "0.470000 0.303869 0.149814           0.154055\n",
      "0.480000 0.304621 0.150245           0.154377\n",
      "0.490000 0.305073 0.150527           0.154545\n",
      "0.500000 0.305223 0.150662           0.154562\n",
      "0.510000 0.305073 0.150648           0.154425\n",
      "0.520000 0.304621 0.150484           0.154137\n",
      "0.530000 0.303869 0.150173           0.153696\n",
      "0.540000 0.302817 0.149712           0.153104\n",
      "0.550000 0.301466 0.149104           0.152362\n",
      "0.560000 0.299817 0.148347           0.151470\n",
      "0.570000 0.297873 0.147444           0.150429\n",
      "0.580000 0.295634 0.146394           0.149240\n",
      "0.590000 0.293104 0.145199           0.147905\n",
      "0.600000 0.290285 0.143859           0.146425\n",
      "0.610000 0.287179 0.142377           0.144802\n",
      "0.620000 0.283790 0.140753           0.143037\n",
      "0.630000 0.280120 0.138988           0.141132\n",
      "0.640000 0.276174 0.137085           0.139090\n",
      "0.650000 0.271956 0.135045           0.136911\n",
      "0.660000 0.267469 0.132870           0.134600\n",
      "0.670000 0.262719 0.130562           0.132157\n",
      "0.680000 0.257709 0.128123           0.129585\n",
      "0.690000 0.252444 0.125556           0.126888\n",
      "0.700000 0.246931 0.122863           0.124068\n",
      "0.710000 0.241174 0.120047           0.121127\n",
      "0.720000 0.235179 0.117109           0.118069\n",
      "0.730000 0.228951 0.114054           0.114897\n",
      "0.740000 0.222498 0.110884           0.111614\n",
      "0.750000 0.215826 0.107602           0.108224\n",
      "0.760000 0.208940 0.104211           0.104729\n",
      "0.770000 0.201848 0.100714           0.101134\n",
      "0.780000 0.194557 0.097115           0.097442\n",
      "0.790000 0.187074 0.093418           0.093656\n",
      "0.800000 0.179406 0.089625           0.089781\n",
      "0.810000 0.171561 0.085740           0.085821\n",
      "0.820000 0.163547 0.081768           0.081779\n",
      "0.830000 0.155371 0.077712           0.077659\n",
      "0.840000 0.147043 0.073576           0.073466\n",
      "0.850000 0.138569 0.069364           0.069204\n",
      "0.860000 0.129958 0.065081           0.064877\n",
      "0.870000 0.121219 0.060729           0.060490\n",
      "0.880000 0.112360 0.056314           0.056046\n",
      "0.890000 0.103391 0.051840           0.051551\n",
      "0.900000 0.094319 0.047311           0.047009\n",
      "0.910000 0.085155 0.042731           0.042423\n",
      "0.920000 0.075906 0.038106           0.037800\n",
      "0.930000 0.066582 0.033439           0.033143\n",
      "0.940000 0.057193 0.028735           0.028458\n",
      "0.950000 0.047747 0.023999           0.023748\n",
      "0.960000 0.038255 0.019236           0.019019\n",
      "0.970000 0.028724 0.014450           0.014274\n",
      "0.980000 0.019165 0.009645           0.009520\n",
      "0.990000 0.009587 0.004827           0.004760\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.12\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.010498 0.005114           0.005384\n",
      "0.020000 0.020986 0.010227           0.010759\n",
      "0.030000 0.031453 0.015335           0.016118\n",
      "0.040000 0.041889 0.020432           0.021457\n",
      "0.050000 0.052284 0.025514           0.026770\n",
      "0.060000 0.062627 0.030574           0.032053\n",
      "0.070000 0.072908 0.035608           0.037300\n",
      "0.080000 0.083118 0.040612           0.042506\n",
      "0.090000 0.093245 0.045580           0.047665\n",
      "0.100000 0.103280 0.050507           0.052773\n",
      "0.110000 0.113214 0.055388           0.057826\n",
      "0.120000 0.123035 0.060219           0.062817\n",
      "0.130000 0.132736 0.064994           0.067742\n",
      "0.140000 0.142305 0.069709           0.072596\n",
      "0.150000 0.151734 0.074359           0.077375\n",
      "0.160000 0.161013 0.078939           0.082074\n",
      "0.170000 0.170133 0.083445           0.086688\n",
      "0.180000 0.179085 0.087873           0.091213\n",
      "0.190000 0.187861 0.092217           0.095644\n",
      "0.200000 0.196451 0.096474           0.099977\n",
      "0.210000 0.204847 0.100638           0.104209\n",
      "0.220000 0.213041 0.104707           0.108334\n",
      "0.230000 0.221025 0.108676           0.112349\n",
      "0.240000 0.228791 0.112540           0.116251\n",
      "0.250000 0.236331 0.116297           0.120034\n",
      "0.260000 0.243638 0.119941           0.123696\n",
      "0.270000 0.250704 0.123470           0.127234\n",
      "0.280000 0.257523 0.126880           0.130643\n",
      "0.290000 0.264087 0.130167           0.133920\n",
      "0.300000 0.270392 0.133329           0.137063\n",
      "0.310000 0.276429 0.136361           0.140068\n",
      "0.320000 0.282193 0.139260           0.142933\n",
      "0.330000 0.287679 0.142025           0.145654\n",
      "0.340000 0.292881 0.144651           0.148230\n",
      "0.350000 0.297794 0.147137           0.150658\n",
      "0.360000 0.302413 0.149479           0.152935\n",
      "0.370000 0.306734 0.151675           0.155059\n",
      "0.380000 0.310752 0.153723           0.157029\n",
      "0.390000 0.314463 0.155621           0.158842\n",
      "0.400000 0.317864 0.157367           0.160498\n",
      "0.410000 0.320952 0.158958           0.161993\n",
      "0.420000 0.323722 0.160394           0.163328\n",
      "0.430000 0.326173 0.161673           0.164500\n",
      "0.440000 0.328302 0.162793           0.165510\n",
      "0.450000 0.330107 0.163752           0.166355\n",
      "0.460000 0.331587 0.164551           0.167035\n",
      "0.470000 0.332739 0.165188           0.167551\n",
      "0.480000 0.333563 0.165663           0.167900\n",
      "0.490000 0.334057 0.165974           0.168083\n",
      "0.500000 0.334222 0.166121           0.168101\n",
      "0.510000 0.334057 0.166105           0.167953\n",
      "0.520000 0.333563 0.165924           0.167639\n",
      "0.530000 0.332739 0.165580           0.167159\n",
      "0.540000 0.331587 0.165071           0.166516\n",
      "0.550000 0.330107 0.164399           0.165708\n",
      "0.560000 0.328302 0.163565           0.164737\n",
      "0.570000 0.326173 0.162568           0.163605\n",
      "0.580000 0.323722 0.161410           0.162312\n",
      "0.590000 0.320952 0.160091           0.160860\n",
      "0.600000 0.317864 0.158614           0.159250\n",
      "0.610000 0.314463 0.156979           0.157485\n",
      "0.620000 0.310752 0.155187           0.155565\n",
      "0.630000 0.306734 0.153241           0.153493\n",
      "0.640000 0.302413 0.151142           0.151272\n",
      "0.650000 0.297794 0.148892           0.148902\n",
      "0.660000 0.292881 0.146493           0.146388\n",
      "0.670000 0.287679 0.143948           0.143731\n",
      "0.680000 0.282193 0.141259           0.140935\n",
      "0.690000 0.276429 0.138428           0.138001\n",
      "0.700000 0.270392 0.135458           0.134933\n",
      "0.710000 0.264087 0.132352           0.131735\n",
      "0.720000 0.257523 0.129113           0.128409\n",
      "0.730000 0.250704 0.125744           0.124959\n",
      "0.740000 0.243638 0.122249           0.121389\n",
      "0.750000 0.236331 0.118630           0.117701\n",
      "0.760000 0.228791 0.114890           0.113900\n",
      "0.770000 0.221025 0.111035           0.109990\n",
      "0.780000 0.213041 0.107067           0.105974\n",
      "0.790000 0.204847 0.102990           0.101857\n",
      "0.800000 0.196451 0.098808           0.097643\n",
      "0.810000 0.187861 0.094525           0.093336\n",
      "0.820000 0.179085 0.090146           0.088940\n",
      "0.830000 0.170133 0.085674           0.084459\n",
      "0.840000 0.161013 0.081114           0.079899\n",
      "0.850000 0.151734 0.076470           0.075264\n",
      "0.860000 0.142305 0.071747           0.070558\n",
      "0.870000 0.132736 0.066949           0.065786\n",
      "0.880000 0.123035 0.062082           0.060954\n",
      "0.890000 0.113214 0.057149           0.056065\n",
      "0.900000 0.103280 0.052156           0.051125\n",
      "0.910000 0.093245 0.047107           0.046138\n",
      "0.920000 0.083118 0.042008           0.041110\n",
      "0.930000 0.072908 0.036863           0.036045\n",
      "0.940000 0.062627 0.031678           0.030949\n",
      "0.950000 0.052284 0.026457           0.025827\n",
      "0.960000 0.041889 0.021205           0.020684\n",
      "0.970000 0.031453 0.015929           0.015524\n",
      "0.980000 0.020986 0.010632           0.010354\n",
      "0.990000 0.010498 0.005321           0.005177\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.13\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.011419 0.005605           0.005814\n",
      "0.020000 0.022828 0.011210           0.011617\n",
      "0.030000 0.034213 0.016808           0.017405\n",
      "0.040000 0.045565 0.022395           0.023170\n",
      "0.050000 0.056872 0.027964           0.028908\n",
      "0.060000 0.068123 0.033511           0.034612\n",
      "0.070000 0.079306 0.039029           0.040278\n",
      "0.080000 0.090411 0.044513           0.045899\n",
      "0.090000 0.101427 0.049957           0.051470\n",
      "0.100000 0.112343 0.055357           0.056986\n",
      "0.110000 0.123149 0.060707           0.062442\n",
      "0.120000 0.133832 0.066001           0.067831\n",
      "0.130000 0.144384 0.071234           0.073149\n",
      "0.140000 0.154792 0.076401           0.078391\n",
      "0.150000 0.165049 0.081497           0.083551\n",
      "0.160000 0.175142 0.086517           0.088625\n",
      "0.170000 0.185063 0.091455           0.093607\n",
      "0.180000 0.194800 0.096307           0.098493\n",
      "0.190000 0.204346 0.101068           0.103278\n",
      "0.200000 0.213690 0.105733           0.107957\n",
      "0.210000 0.222823 0.110297           0.112526\n",
      "0.220000 0.231736 0.114755           0.116981\n",
      "0.230000 0.240421 0.119104           0.121316\n",
      "0.240000 0.248868 0.123339           0.125529\n",
      "0.250000 0.257069 0.127455           0.129614\n",
      "0.260000 0.265017 0.131449           0.133568\n",
      "0.270000 0.272704 0.135316           0.137388\n",
      "0.280000 0.280121 0.139052           0.141069\n",
      "0.290000 0.287262 0.142654           0.144608\n",
      "0.300000 0.294119 0.146118           0.148001\n",
      "0.310000 0.300686 0.149440           0.151246\n",
      "0.320000 0.306956 0.152617           0.154339\n",
      "0.330000 0.312924 0.155646           0.157278\n",
      "0.340000 0.318582 0.158523           0.160059\n",
      "0.350000 0.323926 0.161246           0.162680\n",
      "0.360000 0.328951 0.163812           0.165139\n",
      "0.370000 0.333651 0.166218           0.167432\n",
      "0.380000 0.338021 0.168462           0.169559\n",
      "0.390000 0.342058 0.170541           0.171517\n",
      "0.400000 0.345758 0.172453           0.173304\n",
      "0.410000 0.349116 0.174197           0.174919\n",
      "0.420000 0.352129 0.175769           0.176360\n",
      "0.430000 0.354796 0.177169           0.177626\n",
      "0.440000 0.357112 0.178396           0.178716\n",
      "0.450000 0.359075 0.179447           0.179628\n",
      "0.460000 0.360684 0.180321           0.180363\n",
      "0.470000 0.361938 0.181019           0.180919\n",
      "0.480000 0.362834 0.181538           0.181296\n",
      "0.490000 0.363372 0.181878           0.181494\n",
      "0.500000 0.363551 0.182038           0.181513\n",
      "0.510000 0.363372 0.182019           0.181352\n",
      "0.520000 0.362834 0.181821           0.181013\n",
      "0.530000 0.361938 0.181442           0.180495\n",
      "0.540000 0.360684 0.180884           0.179800\n",
      "0.550000 0.359075 0.180147           0.178928\n",
      "0.560000 0.357112 0.179232           0.177880\n",
      "0.570000 0.354796 0.178139           0.176657\n",
      "0.580000 0.352129 0.176869           0.175261\n",
      "0.590000 0.349116 0.175423           0.173693\n",
      "0.600000 0.345758 0.173803           0.171954\n",
      "0.610000 0.342058 0.172011           0.170048\n",
      "0.620000 0.338021 0.170047           0.167975\n",
      "0.630000 0.333651 0.167913           0.165737\n",
      "0.640000 0.328951 0.165612           0.163338\n",
      "0.650000 0.323926 0.163146           0.160780\n",
      "0.660000 0.318582 0.160517           0.158065\n",
      "0.670000 0.312924 0.157728           0.155196\n",
      "0.680000 0.306956 0.154780           0.152176\n",
      "0.690000 0.300686 0.151678           0.149008\n",
      "0.700000 0.294119 0.148423           0.145696\n",
      "0.710000 0.287262 0.145019           0.142242\n",
      "0.720000 0.280121 0.141470           0.138651\n",
      "0.730000 0.272704 0.137778           0.134926\n",
      "0.740000 0.265017 0.133947           0.131070\n",
      "0.750000 0.257069 0.129981           0.127089\n",
      "0.760000 0.248868 0.125883           0.122985\n",
      "0.770000 0.240421 0.121658           0.118762\n",
      "0.780000 0.231736 0.117310           0.114426\n",
      "0.790000 0.222823 0.112842           0.109981\n",
      "0.800000 0.213690 0.108260           0.105430\n",
      "0.810000 0.204346 0.103567           0.100779\n",
      "0.820000 0.194800 0.098768           0.096032\n",
      "0.830000 0.185063 0.093868           0.091195\n",
      "0.840000 0.175142 0.088871           0.086271\n",
      "0.850000 0.165049 0.083783           0.081266\n",
      "0.860000 0.154792 0.078608           0.076185\n",
      "0.870000 0.144384 0.073351           0.071032\n",
      "0.880000 0.133832 0.068018           0.065814\n",
      "0.890000 0.123149 0.062613           0.060535\n",
      "0.900000 0.112343 0.057142           0.055201\n",
      "0.910000 0.101427 0.051611           0.049817\n",
      "0.920000 0.090411 0.046024           0.044388\n",
      "0.930000 0.079306 0.040387           0.038919\n",
      "0.940000 0.068123 0.034705           0.033417\n",
      "0.950000 0.056872 0.028985           0.027887\n",
      "0.960000 0.045565 0.023232           0.022333\n",
      "0.970000 0.034213 0.017451           0.016762\n",
      "0.980000 0.022828 0.011648           0.011179\n",
      "0.990000 0.011419 0.005829           0.005590\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.14\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.012352 0.006112           0.006240\n",
      "0.020000 0.024692 0.012224           0.012468\n",
      "0.030000 0.037007 0.018329           0.018678\n",
      "0.040000 0.049286 0.024420           0.024866\n",
      "0.050000 0.061516 0.030493           0.031023\n",
      "0.060000 0.073686 0.036541           0.037145\n",
      "0.070000 0.085782 0.042557           0.043225\n",
      "0.080000 0.097794 0.048537           0.049258\n",
      "0.090000 0.109710 0.054473           0.055237\n",
      "0.100000 0.121517 0.060361           0.061156\n",
      "0.110000 0.133205 0.066194           0.067011\n",
      "0.120000 0.144761 0.071966           0.072795\n",
      "0.130000 0.156174 0.077672           0.078502\n",
      "0.140000 0.167433 0.083306           0.084127\n",
      "0.150000 0.178527 0.088862           0.089665\n",
      "0.160000 0.189444 0.094334           0.095110\n",
      "0.170000 0.200175 0.099718           0.100456\n",
      "0.180000 0.210708 0.105008           0.105700\n",
      "0.190000 0.221033 0.110198           0.110835\n",
      "0.200000 0.231140 0.115284           0.115856\n",
      "0.210000 0.241019 0.120259           0.120759\n",
      "0.220000 0.250660 0.125120           0.125539\n",
      "0.230000 0.260053 0.129861           0.130192\n",
      "0.240000 0.269190 0.134478           0.134713\n",
      "0.250000 0.278062 0.138965           0.139097\n",
      "0.260000 0.286659 0.143319           0.143340\n",
      "0.270000 0.294973 0.147534           0.147439\n",
      "0.280000 0.302996 0.151607           0.151389\n",
      "0.290000 0.310719 0.155533           0.155187\n",
      "0.300000 0.318137 0.159309           0.158828\n",
      "0.310000 0.325240 0.162930           0.162310\n",
      "0.320000 0.332022 0.166393           0.165630\n",
      "0.330000 0.338477 0.169694           0.168783\n",
      "0.340000 0.344598 0.172830           0.171767\n",
      "0.350000 0.350378 0.175798           0.174580\n",
      "0.360000 0.355813 0.178595           0.177218\n",
      "0.370000 0.360897 0.181217           0.179679\n",
      "0.380000 0.365624 0.183662           0.181961\n",
      "0.390000 0.369991 0.185928           0.184062\n",
      "0.400000 0.373992 0.188012           0.185980\n",
      "0.410000 0.377625 0.189912           0.187713\n",
      "0.420000 0.380884 0.191625           0.189259\n",
      "0.430000 0.383768 0.193151           0.190617\n",
      "0.440000 0.386273 0.194487           0.191786\n",
      "0.450000 0.388397 0.195632           0.192765\n",
      "0.460000 0.390138 0.196584           0.193554\n",
      "0.470000 0.391493 0.197343           0.194150\n",
      "0.480000 0.392463 0.197908           0.194555\n",
      "0.490000 0.393045 0.198278           0.194767\n",
      "0.500000 0.393239 0.198452           0.194787\n",
      "0.510000 0.393045 0.198430           0.194614\n",
      "0.520000 0.392463 0.198213           0.194250\n",
      "0.530000 0.391493 0.197799           0.193694\n",
      "0.540000 0.390138 0.197190           0.192948\n",
      "0.550000 0.388397 0.196385           0.192012\n",
      "0.560000 0.386273 0.195386           0.190887\n",
      "0.570000 0.383768 0.194194           0.189574\n",
      "0.580000 0.380884 0.192808           0.188076\n",
      "0.590000 0.377625 0.191232           0.186393\n",
      "0.600000 0.373992 0.189465           0.184527\n",
      "0.610000 0.369991 0.187510           0.182481\n",
      "0.620000 0.365624 0.185368           0.180256\n",
      "0.630000 0.360897 0.183041           0.177855\n",
      "0.640000 0.355813 0.180532           0.175281\n",
      "0.650000 0.350378 0.177843           0.172535\n",
      "0.660000 0.344598 0.174976           0.169621\n",
      "0.670000 0.338477 0.171935           0.166542\n",
      "0.680000 0.332022 0.168721           0.163301\n",
      "0.690000 0.325240 0.165338           0.159902\n",
      "0.700000 0.318137 0.161789           0.156347\n",
      "0.710000 0.310719 0.158078           0.152641\n",
      "0.720000 0.302996 0.154208           0.148787\n",
      "0.730000 0.294973 0.150183           0.144789\n",
      "0.740000 0.286659 0.146007           0.140652\n",
      "0.750000 0.278062 0.141683           0.136379\n",
      "0.760000 0.269190 0.137216           0.131975\n",
      "0.770000 0.260053 0.132610           0.127444\n",
      "0.780000 0.250660 0.127869           0.122791\n",
      "0.790000 0.241019 0.122999           0.118020\n",
      "0.800000 0.231140 0.118003           0.113137\n",
      "0.810000 0.221033 0.112887           0.108145\n",
      "0.820000 0.210708 0.107656           0.103052\n",
      "0.830000 0.200175 0.102315           0.097860\n",
      "0.840000 0.189444 0.096868           0.092576\n",
      "0.850000 0.178527 0.091321           0.087205\n",
      "0.860000 0.167433 0.085680           0.081753\n",
      "0.870000 0.156174 0.079950           0.076224\n",
      "0.880000 0.144761 0.074136           0.070624\n",
      "0.890000 0.133205 0.068245           0.064960\n",
      "0.900000 0.121517 0.062282           0.059236\n",
      "0.910000 0.109710 0.056252           0.053458\n",
      "0.920000 0.097794 0.050163           0.047632\n",
      "0.930000 0.085782 0.044019           0.041764\n",
      "0.940000 0.073686 0.037826           0.035859\n",
      "0.950000 0.061516 0.031592           0.029924\n",
      "0.960000 0.049286 0.025321           0.023965\n",
      "0.970000 0.037007 0.019020           0.017987\n",
      "0.980000 0.024692 0.012696           0.011996\n",
      "0.990000 0.012352 0.006353           0.005998\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.15\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.013297 0.006636           0.006660\n",
      "0.020000 0.026580 0.013271           0.013309\n",
      "0.030000 0.039837 0.019899           0.019938\n",
      "0.040000 0.053055 0.026513           0.026543\n",
      "0.050000 0.066221 0.033105           0.033115\n",
      "0.060000 0.079321 0.039671           0.039650\n",
      "0.070000 0.092343 0.046203           0.046140\n",
      "0.080000 0.105274 0.052694           0.052580\n",
      "0.090000 0.118101 0.059139           0.058962\n",
      "0.100000 0.130811 0.065531           0.065281\n",
      "0.110000 0.143393 0.071863           0.071530\n",
      "0.120000 0.155832 0.078129           0.077704\n",
      "0.130000 0.168118 0.084323           0.083796\n",
      "0.140000 0.180238 0.090438           0.089800\n",
      "0.150000 0.192181 0.096470           0.095711\n",
      "0.160000 0.203933 0.102410           0.101523\n",
      "0.170000 0.215484 0.108254           0.107230\n",
      "0.180000 0.226823 0.113996           0.112827\n",
      "0.190000 0.237938 0.119630           0.118308\n",
      "0.200000 0.248818 0.125150           0.123668\n",
      "0.210000 0.259452 0.130551           0.128901\n",
      "0.220000 0.269831 0.135827           0.134004\n",
      "0.230000 0.279943 0.140973           0.138970\n",
      "0.240000 0.289779 0.145984           0.143795\n",
      "0.250000 0.299328 0.150854           0.148474\n",
      "0.260000 0.308583 0.155579           0.153004\n",
      "0.270000 0.317533 0.160154           0.157379\n",
      "0.280000 0.326169 0.164575           0.161595\n",
      "0.290000 0.334484 0.168836           0.165648\n",
      "0.300000 0.342468 0.172933           0.169535\n",
      "0.310000 0.350115 0.176863           0.173252\n",
      "0.320000 0.357416 0.180621           0.176795\n",
      "0.330000 0.364364 0.184204           0.180160\n",
      "0.340000 0.370953 0.187608           0.183346\n",
      "0.350000 0.377176 0.190828           0.186348\n",
      "0.360000 0.383026 0.193863           0.189163\n",
      "0.370000 0.388499 0.196708           0.191790\n",
      "0.380000 0.393588 0.199362           0.194226\n",
      "0.390000 0.398288 0.201820           0.196468\n",
      "0.400000 0.402596 0.204081           0.198515\n",
      "0.410000 0.406506 0.206142           0.200364\n",
      "0.420000 0.410015 0.208001           0.202015\n",
      "0.430000 0.413119 0.209655           0.203464\n",
      "0.440000 0.415816 0.211104           0.204712\n",
      "0.450000 0.418103 0.212346           0.205757\n",
      "0.460000 0.419976 0.213379           0.206598\n",
      "0.470000 0.421436 0.214201           0.207234\n",
      "0.480000 0.422479 0.214813           0.207666\n",
      "0.490000 0.423105 0.215214           0.207892\n",
      "0.500000 0.423314 0.215401           0.207913\n",
      "0.510000 0.423105 0.215377           0.207729\n",
      "0.520000 0.422479 0.215139           0.207340\n",
      "0.530000 0.421436 0.214689           0.206746\n",
      "0.540000 0.419976 0.214027           0.205949\n",
      "0.550000 0.418103 0.213153           0.204950\n",
      "0.560000 0.415816 0.212067           0.203749\n",
      "0.570000 0.413119 0.210772           0.202348\n",
      "0.580000 0.410015 0.209267           0.200748\n",
      "0.590000 0.406506 0.207555           0.198951\n",
      "0.600000 0.402596 0.205636           0.196960\n",
      "0.610000 0.398288 0.203513           0.194775\n",
      "0.620000 0.393588 0.201187           0.192401\n",
      "0.630000 0.388499 0.198661           0.189838\n",
      "0.640000 0.383026 0.195937           0.187089\n",
      "0.650000 0.377176 0.193017           0.184158\n",
      "0.660000 0.370953 0.189905           0.181048\n",
      "0.670000 0.364364 0.186603           0.177762\n",
      "0.680000 0.357416 0.183114           0.174302\n",
      "0.690000 0.350115 0.179441           0.170674\n",
      "0.700000 0.342468 0.175589           0.166879\n",
      "0.710000 0.334484 0.171561           0.162923\n",
      "0.720000 0.326169 0.167360           0.158810\n",
      "0.730000 0.317533 0.162990           0.154542\n",
      "0.740000 0.308583 0.158457           0.150126\n",
      "0.750000 0.299328 0.153763           0.145565\n",
      "0.760000 0.289779 0.148915           0.140864\n",
      "0.770000 0.279943 0.143915           0.136028\n",
      "0.780000 0.269831 0.138770           0.131061\n",
      "0.790000 0.259452 0.133484           0.125969\n",
      "0.800000 0.248818 0.128062           0.120756\n",
      "0.810000 0.237938 0.122509           0.115429\n",
      "0.820000 0.226823 0.116831           0.109992\n",
      "0.830000 0.215484 0.111034           0.104451\n",
      "0.840000 0.203933 0.105122           0.098811\n",
      "0.850000 0.192181 0.099102           0.093078\n",
      "0.860000 0.180238 0.092980           0.087258\n",
      "0.870000 0.168118 0.086761           0.081357\n",
      "0.880000 0.155832 0.080452           0.075380\n",
      "0.890000 0.143393 0.074059           0.069334\n",
      "0.900000 0.130811 0.067587           0.063224\n",
      "0.910000 0.118101 0.061044           0.057057\n",
      "0.920000 0.105274 0.054435           0.050839\n",
      "0.930000 0.092343 0.047767           0.044576\n",
      "0.940000 0.079321 0.041047           0.038274\n",
      "0.950000 0.066221 0.034282           0.031939\n",
      "0.960000 0.053055 0.027477           0.025579\n",
      "0.970000 0.039837 0.020639           0.019198\n",
      "0.980000 0.026580 0.013776           0.012804\n",
      "0.990000 0.013297 0.006894           0.006402\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.16\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.014254 0.007178           0.007076\n",
      "0.020000 0.028495 0.014355           0.014140\n",
      "0.030000 0.042707 0.021524           0.021183\n",
      "0.040000 0.056877 0.028677           0.028200\n",
      "0.050000 0.070991 0.035808           0.035183\n",
      "0.060000 0.085035 0.042910           0.042126\n",
      "0.070000 0.098995 0.049974           0.049021\n",
      "0.080000 0.112857 0.056995           0.055862\n",
      "0.090000 0.126608 0.063966           0.062643\n",
      "0.100000 0.140234 0.070878           0.069356\n",
      "0.110000 0.153722 0.077727           0.075995\n",
      "0.120000 0.167058 0.084504           0.082554\n",
      "0.130000 0.180229 0.091202           0.089026\n",
      "0.140000 0.193222 0.097816           0.095406\n",
      "0.150000 0.206024 0.104339           0.101685\n",
      "0.160000 0.218624 0.110764           0.107860\n",
      "0.170000 0.231007 0.117084           0.113923\n",
      "0.180000 0.243162 0.123293           0.119869\n",
      "0.190000 0.255078 0.129386           0.125692\n",
      "0.200000 0.266742 0.135355           0.131386\n",
      "0.210000 0.278142 0.141196           0.136946\n",
      "0.220000 0.289268 0.146901           0.142367\n",
      "0.230000 0.300108 0.152466           0.147643\n",
      "0.240000 0.310653 0.157884           0.152769\n",
      "0.250000 0.320891 0.163151           0.157740\n",
      "0.260000 0.330812 0.168260           0.162552\n",
      "0.270000 0.340406 0.173207           0.167200\n",
      "0.280000 0.349665 0.177986           0.171679\n",
      "0.290000 0.358579 0.182594           0.175985\n",
      "0.300000 0.367138 0.187024           0.180114\n",
      "0.310000 0.375336 0.191273           0.184062\n",
      "0.320000 0.383163 0.195337           0.187826\n",
      "0.330000 0.390611 0.199210           0.191401\n",
      "0.340000 0.397675 0.202890           0.194785\n",
      "0.350000 0.404346 0.206371           0.197974\n",
      "0.360000 0.410618 0.209652           0.200966\n",
      "0.370000 0.416484 0.212728           0.203756\n",
      "0.380000 0.421940 0.215596           0.206344\n",
      "0.390000 0.426979 0.218253           0.208726\n",
      "0.400000 0.431597 0.220697           0.210900\n",
      "0.410000 0.435789 0.222925           0.212864\n",
      "0.420000 0.439551 0.224934           0.214617\n",
      "0.430000 0.442879 0.226722           0.216157\n",
      "0.440000 0.445770 0.228288           0.217482\n",
      "0.450000 0.448221 0.229629           0.218592\n",
      "0.460000 0.450229 0.230744           0.219485\n",
      "0.470000 0.451794 0.231633           0.220161\n",
      "0.480000 0.452912 0.232293           0.220619\n",
      "0.490000 0.453584 0.232725           0.220859\n",
      "0.500000 0.453808 0.232927           0.220881\n",
      "0.510000 0.453584 0.232899           0.220685\n",
      "0.520000 0.452912 0.232641           0.220272\n",
      "0.530000 0.451794 0.232153           0.219641\n",
      "0.540000 0.450229 0.231435           0.218794\n",
      "0.550000 0.448221 0.230489           0.217732\n",
      "0.560000 0.445770 0.229314           0.216456\n",
      "0.570000 0.442879 0.227912           0.214967\n",
      "0.580000 0.439551 0.226283           0.213267\n",
      "0.590000 0.435789 0.224430           0.211358\n",
      "0.600000 0.431597 0.222354           0.209242\n",
      "0.610000 0.426979 0.220058           0.206922\n",
      "0.620000 0.421940 0.217542           0.204398\n",
      "0.630000 0.416484 0.214809           0.201675\n",
      "0.640000 0.410618 0.211862           0.198755\n",
      "0.650000 0.404346 0.208704           0.195642\n",
      "0.660000 0.397675 0.205338           0.192337\n",
      "0.670000 0.390611 0.201766           0.188845\n",
      "0.680000 0.383163 0.197992           0.185170\n",
      "0.690000 0.375336 0.194021           0.181315\n",
      "0.700000 0.367138 0.189854           0.177284\n",
      "0.710000 0.358579 0.185497           0.173081\n",
      "0.720000 0.349665 0.180954           0.168711\n",
      "0.730000 0.340406 0.176229           0.164177\n",
      "0.740000 0.330812 0.171326           0.159485\n",
      "0.750000 0.320891 0.166251           0.154640\n",
      "0.760000 0.310653 0.161007           0.149645\n",
      "0.770000 0.300108 0.155601           0.144507\n",
      "0.780000 0.289268 0.150037           0.139231\n",
      "0.790000 0.278142 0.144321           0.133821\n",
      "0.800000 0.266742 0.138458           0.128284\n",
      "0.810000 0.255078 0.132454           0.122624\n",
      "0.820000 0.243162 0.126314           0.116848\n",
      "0.830000 0.231007 0.120046           0.110961\n",
      "0.840000 0.218624 0.113654           0.104970\n",
      "0.850000 0.206024 0.107145           0.098880\n",
      "0.860000 0.193222 0.100525           0.092697\n",
      "0.870000 0.180229 0.093801           0.086428\n",
      "0.880000 0.167058 0.086979           0.080078\n",
      "0.890000 0.153722 0.080067           0.073655\n",
      "0.900000 0.140234 0.073070           0.067165\n",
      "0.910000 0.126608 0.065995           0.060613\n",
      "0.920000 0.112857 0.058850           0.054007\n",
      "0.930000 0.098995 0.051641           0.047354\n",
      "0.940000 0.085035 0.044376           0.040659\n",
      "0.950000 0.070991 0.037062           0.033930\n",
      "0.960000 0.056877 0.029705           0.027172\n",
      "0.970000 0.042707 0.022313           0.020394\n",
      "0.980000 0.028495 0.014893           0.013602\n",
      "0.990000 0.014254 0.007453           0.006801\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.17\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.015226 0.007740           0.007487\n",
      "0.020000 0.030438 0.015478           0.014960\n",
      "0.030000 0.045619 0.023207           0.022412\n",
      "0.040000 0.060755 0.030919           0.029836\n",
      "0.050000 0.075831 0.038607           0.037224\n",
      "0.060000 0.090833 0.046264           0.044569\n",
      "0.070000 0.105745 0.053880           0.051865\n",
      "0.080000 0.120552 0.061450           0.059103\n",
      "0.090000 0.135241 0.068964           0.066276\n",
      "0.100000 0.149796 0.076417           0.073379\n",
      "0.110000 0.164203 0.083800           0.080403\n",
      "0.120000 0.178448 0.091106           0.087343\n",
      "0.130000 0.192517 0.098327           0.094190\n",
      "0.140000 0.206396 0.105457           0.100939\n",
      "0.150000 0.220072 0.112489           0.107583\n",
      "0.160000 0.233530 0.119414           0.114115\n",
      "0.170000 0.246757 0.126227           0.120530\n",
      "0.180000 0.259742 0.132921           0.126821\n",
      "0.190000 0.272469 0.139488           0.132981\n",
      "0.200000 0.284928 0.145923           0.139005\n",
      "0.210000 0.297106 0.152219           0.144888\n",
      "0.220000 0.308991 0.158368           0.150622\n",
      "0.230000 0.320570 0.164366           0.156204\n",
      "0.240000 0.331834 0.170207           0.161627\n",
      "0.250000 0.342769 0.175883           0.166887\n",
      "0.260000 0.353367 0.181390           0.171977\n",
      "0.270000 0.363616 0.186722           0.176894\n",
      "0.280000 0.373506 0.191873           0.181633\n",
      "0.290000 0.383027 0.196839           0.186188\n",
      "0.300000 0.392170 0.201614           0.190557\n",
      "0.310000 0.400927 0.206193           0.194734\n",
      "0.320000 0.409287 0.210572           0.198715\n",
      "0.330000 0.417244 0.214746           0.202498\n",
      "0.340000 0.424789 0.218712           0.206077\n",
      "0.350000 0.431915 0.222464           0.209451\n",
      "0.360000 0.438614 0.225999           0.212615\n",
      "0.370000 0.444881 0.229313           0.215568\n",
      "0.380000 0.450708 0.232404           0.218305\n",
      "0.390000 0.456091 0.235267           0.220825\n",
      "0.400000 0.461024 0.237900           0.223124\n",
      "0.410000 0.465502 0.240299           0.225202\n",
      "0.420000 0.469520 0.242463           0.227056\n",
      "0.430000 0.473075 0.244390           0.228685\n",
      "0.440000 0.476163 0.246076           0.230087\n",
      "0.450000 0.478781 0.247520           0.231261\n",
      "0.460000 0.480927 0.248722           0.232205\n",
      "0.470000 0.482598 0.249678           0.232920\n",
      "0.480000 0.483793 0.250388           0.233405\n",
      "0.490000 0.484510 0.250852           0.233658\n",
      "0.500000 0.484749 0.251068           0.233681\n",
      "0.510000 0.484510 0.251036           0.233474\n",
      "0.520000 0.483793 0.250757           0.233036\n",
      "0.530000 0.482598 0.250230           0.232368\n",
      "0.540000 0.480927 0.249455           0.231472\n",
      "0.550000 0.478781 0.248433           0.230348\n",
      "0.560000 0.476163 0.247165           0.228998\n",
      "0.570000 0.473075 0.245653           0.227422\n",
      "0.580000 0.469520 0.243896           0.225624\n",
      "0.590000 0.465502 0.241898           0.223604\n",
      "0.600000 0.461024 0.239659           0.221365\n",
      "0.610000 0.456091 0.237182           0.218910\n",
      "0.620000 0.450708 0.234469           0.216240\n",
      "0.630000 0.444881 0.231522           0.213359\n",
      "0.640000 0.438614 0.228345           0.210270\n",
      "0.650000 0.431915 0.224940           0.206975\n",
      "0.660000 0.424789 0.221310           0.203479\n",
      "0.670000 0.417244 0.217459           0.199785\n",
      "0.680000 0.409287 0.213391           0.195896\n",
      "0.690000 0.400927 0.209109           0.191818\n",
      "0.700000 0.392170 0.204618           0.187553\n",
      "0.710000 0.383027 0.199921           0.183106\n",
      "0.720000 0.373506 0.195023           0.178483\n",
      "0.730000 0.363616 0.189929           0.173686\n",
      "0.740000 0.353367 0.184645           0.168722\n",
      "0.750000 0.342769 0.179173           0.163596\n",
      "0.760000 0.331834 0.173521           0.158312\n",
      "0.770000 0.320570 0.167694           0.152876\n",
      "0.780000 0.308991 0.161697           0.147294\n",
      "0.790000 0.297106 0.155535           0.141571\n",
      "0.800000 0.284928 0.149216           0.135713\n",
      "0.810000 0.272469 0.142744           0.129725\n",
      "0.820000 0.259742 0.136127           0.123614\n",
      "0.830000 0.246757 0.129371           0.117387\n",
      "0.840000 0.233530 0.122482           0.111048\n",
      "0.850000 0.220072 0.115466           0.104605\n",
      "0.860000 0.206396 0.108332           0.098064\n",
      "0.870000 0.192517 0.101085           0.091432\n",
      "0.880000 0.178448 0.093733           0.084715\n",
      "0.890000 0.164203 0.086283           0.077920\n",
      "0.900000 0.149796 0.078742           0.071053\n",
      "0.910000 0.135241 0.071118           0.064122\n",
      "0.920000 0.120552 0.063418           0.057134\n",
      "0.930000 0.105745 0.055650           0.050095\n",
      "0.940000 0.090833 0.047820           0.043013\n",
      "0.950000 0.075831 0.039938           0.035894\n",
      "0.960000 0.060755 0.032010           0.028745\n",
      "0.970000 0.045619 0.024044           0.021575\n",
      "0.980000 0.030438 0.016049           0.014389\n",
      "0.990000 0.015226 0.008031           0.007195\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.18\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.016213 0.008322           0.007892\n",
      "0.020000 0.032411 0.016641           0.015769\n",
      "0.030000 0.048576 0.024952           0.023624\n",
      "0.040000 0.064693 0.033244           0.031449\n",
      "0.050000 0.080747 0.041510           0.039237\n",
      "0.060000 0.096720 0.049741           0.046980\n",
      "0.070000 0.112599 0.057930           0.054669\n",
      "0.080000 0.128366 0.066067           0.062299\n",
      "0.090000 0.144007 0.074146           0.069860\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.100000 0.159505 0.082158           0.077347\n",
      "0.110000 0.174846 0.090095           0.084751\n",
      "0.120000 0.190015 0.097950           0.092065\n",
      "0.130000 0.204996 0.105713           0.099283\n",
      "0.140000 0.219774 0.113378           0.106396\n",
      "0.150000 0.234336 0.120937           0.113399\n",
      "0.160000 0.248666 0.128382           0.120285\n",
      "0.170000 0.262751 0.135706           0.127046\n",
      "0.180000 0.276577 0.142901           0.133676\n",
      "0.190000 0.290130 0.149961           0.140170\n",
      "0.200000 0.303397 0.156877           0.146519\n",
      "0.210000 0.316364 0.163644           0.152719\n",
      "0.220000 0.329019 0.170255           0.158764\n",
      "0.230000 0.341349 0.176702           0.164647\n",
      "0.240000 0.353342 0.182979           0.170363\n",
      "0.250000 0.364987 0.189080           0.175906\n",
      "0.260000 0.376271 0.194999           0.181272\n",
      "0.270000 0.387184 0.200730           0.186454\n",
      "0.280000 0.397715 0.206266           0.191449\n",
      "0.290000 0.407854 0.211603           0.196250\n",
      "0.300000 0.417590 0.216735           0.200854\n",
      "0.310000 0.426914 0.221657           0.205257\n",
      "0.320000 0.435816 0.226363           0.209453\n",
      "0.330000 0.444289 0.230849           0.213440\n",
      "0.340000 0.452323 0.235110           0.217213\n",
      "0.350000 0.459910 0.239142           0.220768\n",
      "0.360000 0.467044 0.242940           0.224104\n",
      "0.370000 0.473717 0.246502           0.227215\n",
      "0.380000 0.479922 0.249822           0.230100\n",
      "0.390000 0.485654 0.252898           0.232755\n",
      "0.400000 0.490906 0.255727           0.235179\n",
      "0.410000 0.495674 0.258305           0.237369\n",
      "0.420000 0.499953 0.260630           0.239323\n",
      "0.430000 0.503738 0.262699           0.241039\n",
      "0.440000 0.507026 0.264510           0.242517\n",
      "0.450000 0.509814 0.266061           0.243753\n",
      "0.460000 0.512099 0.267350           0.244749\n",
      "0.470000 0.513878 0.268377           0.245502\n",
      "0.480000 0.515151 0.269139           0.246012\n",
      "0.490000 0.515914 0.269635           0.246279\n",
      "0.500000 0.516169 0.269866           0.246303\n",
      "0.510000 0.515914 0.269831           0.246084\n",
      "0.520000 0.515151 0.269529           0.245622\n",
      "0.530000 0.513878 0.268960           0.244918\n",
      "0.540000 0.512099 0.268126           0.243973\n",
      "0.550000 0.509814 0.267026           0.242788\n",
      "0.560000 0.507026 0.265662           0.241365\n",
      "0.570000 0.503738 0.264034           0.239704\n",
      "0.580000 0.499953 0.262145           0.237808\n",
      "0.590000 0.495674 0.259995           0.235679\n",
      "0.600000 0.490906 0.257587           0.233319\n",
      "0.610000 0.485654 0.254924           0.230730\n",
      "0.620000 0.479922 0.252006           0.227916\n",
      "0.630000 0.473717 0.248838           0.224879\n",
      "0.640000 0.467044 0.245421           0.221623\n",
      "0.650000 0.459910 0.241760           0.218150\n",
      "0.660000 0.452323 0.237858           0.214465\n",
      "0.670000 0.444289 0.233718           0.210571\n",
      "0.680000 0.435816 0.229344           0.206472\n",
      "0.690000 0.426914 0.224740           0.202173\n",
      "0.700000 0.417590 0.219912           0.197678\n",
      "0.710000 0.407854 0.214863           0.192991\n",
      "0.720000 0.397715 0.209598           0.188117\n",
      "0.730000 0.387184 0.204122           0.183062\n",
      "0.740000 0.376271 0.198441           0.177830\n",
      "0.750000 0.364987 0.192560           0.172427\n",
      "0.760000 0.353342 0.186485           0.166857\n",
      "0.770000 0.341349 0.180221           0.161128\n",
      "0.780000 0.329019 0.173775           0.155244\n",
      "0.790000 0.316364 0.167152           0.149212\n",
      "0.800000 0.303397 0.160360           0.143037\n",
      "0.810000 0.290130 0.153404           0.136726\n",
      "0.820000 0.276577 0.146292           0.130286\n",
      "0.830000 0.262751 0.139030           0.123722\n",
      "0.840000 0.248666 0.131626           0.117041\n",
      "0.850000 0.234336 0.124086           0.110250\n",
      "0.860000 0.219774 0.116418           0.103356\n",
      "0.870000 0.204996 0.108630           0.096366\n",
      "0.880000 0.190015 0.100729           0.089286\n",
      "0.890000 0.174846 0.092722           0.082124\n",
      "0.900000 0.159505 0.084618           0.074887\n",
      "0.910000 0.144007 0.076424           0.067582\n",
      "0.920000 0.128366 0.068149           0.060217\n",
      "0.930000 0.112599 0.059801           0.052798\n",
      "0.940000 0.096720 0.051387           0.045333\n",
      "0.950000 0.080747 0.042916           0.037830\n",
      "0.960000 0.064693 0.034397           0.030296\n",
      "0.970000 0.048576 0.025837           0.022739\n",
      "0.980000 0.032411 0.017245           0.015165\n",
      "0.990000 0.016213 0.008630           0.007583\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.19\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.017216 0.008925           0.008291\n",
      "0.020000 0.034415 0.017849           0.016566\n",
      "0.030000 0.051581 0.026762           0.024818\n",
      "0.040000 0.068695 0.035656           0.033039\n",
      "0.050000 0.085742 0.044521           0.041220\n",
      "0.060000 0.102703 0.053349           0.049354\n",
      "0.070000 0.119564 0.062132           0.057432\n",
      "0.080000 0.136307 0.070859           0.065447\n",
      "0.090000 0.152915 0.079524           0.073391\n",
      "0.100000 0.169372 0.088116           0.081256\n",
      "0.110000 0.185662 0.096628           0.089034\n",
      "0.120000 0.201769 0.105051           0.096718\n",
      "0.130000 0.217676 0.113377           0.104300\n",
      "0.140000 0.233369 0.121596           0.111773\n",
      "0.150000 0.248832 0.129702           0.119129\n",
      "0.160000 0.264049 0.137686           0.126363\n",
      "0.170000 0.279005 0.145540           0.133465\n",
      "0.180000 0.293686 0.153255           0.140430\n",
      "0.190000 0.308077 0.160826           0.147252\n",
      "0.200000 0.322164 0.168242           0.153922\n",
      "0.210000 0.335933 0.175498           0.160435\n",
      "0.220000 0.349371 0.182586           0.166785\n",
      "0.230000 0.362464 0.189499           0.172965\n",
      "0.240000 0.375199 0.196230           0.178969\n",
      "0.250000 0.387564 0.202772           0.184792\n",
      "0.260000 0.399547 0.209118           0.190429\n",
      "0.270000 0.411135 0.215262           0.195873\n",
      "0.280000 0.422317 0.221198           0.201119\n",
      "0.290000 0.433083 0.226920           0.206163\n",
      "0.300000 0.443421 0.232422           0.210999\n",
      "0.310000 0.453322 0.237698           0.215624\n",
      "0.320000 0.462775 0.242743           0.220032\n",
      "0.330000 0.471771 0.247552           0.224219\n",
      "0.340000 0.480302 0.252120           0.228183\n",
      "0.350000 0.488359 0.256442           0.231917\n",
      "0.360000 0.495934 0.260514           0.235421\n",
      "0.370000 0.503020 0.264331           0.238689\n",
      "0.380000 0.509609 0.267890           0.241719\n",
      "0.390000 0.515695 0.271187           0.244508\n",
      "0.400000 0.521273 0.274219           0.247054\n",
      "0.410000 0.526336 0.276982           0.249354\n",
      "0.420000 0.530879 0.279473           0.251406\n",
      "0.430000 0.534899 0.281690           0.253209\n",
      "0.440000 0.538390 0.283630           0.254761\n",
      "0.450000 0.541351 0.285291           0.256059\n",
      "0.460000 0.543777 0.286672           0.257105\n",
      "0.470000 0.545666 0.287771           0.257895\n",
      "0.480000 0.547017 0.288586           0.258431\n",
      "0.490000 0.547828 0.289117           0.258711\n",
      "0.500000 0.548099 0.289363           0.258736\n",
      "0.510000 0.547828 0.289323           0.258505\n",
      "0.520000 0.547017 0.288997           0.258020\n",
      "0.530000 0.545666 0.288386           0.257280\n",
      "0.540000 0.543777 0.287490           0.256287\n",
      "0.550000 0.541351 0.286309           0.255042\n",
      "0.560000 0.538390 0.284844           0.253546\n",
      "0.570000 0.534899 0.283097           0.251801\n",
      "0.580000 0.530879 0.281070           0.249809\n",
      "0.590000 0.526336 0.278763           0.247572\n",
      "0.600000 0.521273 0.276180           0.245093\n",
      "0.610000 0.515695 0.273322           0.242373\n",
      "0.620000 0.509609 0.270192           0.239417\n",
      "0.630000 0.503020 0.266794           0.236226\n",
      "0.640000 0.495934 0.263129           0.232805\n",
      "0.650000 0.488359 0.259202           0.229157\n",
      "0.660000 0.480302 0.255017           0.225286\n",
      "0.670000 0.471771 0.250577           0.221195\n",
      "0.680000 0.462775 0.245886           0.216889\n",
      "0.690000 0.453322 0.240949           0.212373\n",
      "0.700000 0.443421 0.235771           0.207650\n",
      "0.710000 0.433083 0.230356           0.202727\n",
      "0.720000 0.422317 0.224710           0.197607\n",
      "0.730000 0.411135 0.218838           0.192296\n",
      "0.740000 0.399547 0.212746           0.186800\n",
      "0.750000 0.387564 0.206440           0.181124\n",
      "0.760000 0.375199 0.199926           0.175274\n",
      "0.770000 0.362464 0.193209           0.169255\n",
      "0.780000 0.349371 0.186297           0.163074\n",
      "0.790000 0.335933 0.179196           0.156737\n",
      "0.800000 0.322164 0.171913           0.150251\n",
      "0.810000 0.308077 0.164455           0.143622\n",
      "0.820000 0.293686 0.156830           0.136856\n",
      "0.830000 0.279005 0.149044           0.129961\n",
      "0.840000 0.264049 0.141105           0.122943\n",
      "0.850000 0.248832 0.133022           0.115810\n",
      "0.860000 0.233369 0.124801           0.108568\n",
      "0.870000 0.217676 0.116451           0.101225\n",
      "0.880000 0.201769 0.107981           0.093788\n",
      "0.890000 0.185662 0.099397           0.086265\n",
      "0.900000 0.169372 0.090709           0.078663\n",
      "0.910000 0.152915 0.081925           0.070989\n",
      "0.920000 0.136307 0.073054           0.063253\n",
      "0.930000 0.119564 0.064104           0.055460\n",
      "0.940000 0.102703 0.055085           0.047619\n",
      "0.950000 0.085742 0.046004           0.039737\n",
      "0.960000 0.068695 0.036872           0.031823\n",
      "0.970000 0.051581 0.027696           0.023885\n",
      "0.980000 0.034415 0.018486           0.015930\n",
      "0.990000 0.017216 0.009251           0.007965\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.2\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.018236 0.009553           0.008683\n",
      "0.020000 0.036454 0.019103           0.017351\n",
      "0.030000 0.054636 0.028643           0.025994\n",
      "0.040000 0.072765 0.038161           0.034604\n",
      "0.050000 0.090821 0.047649           0.043172\n",
      "0.060000 0.108788 0.057097           0.051691\n",
      "0.070000 0.126647 0.066495           0.060152\n",
      "0.080000 0.144382 0.075836           0.068546\n",
      "0.090000 0.161974 0.085108           0.076866\n",
      "0.100000 0.179406 0.094303           0.085103\n",
      "0.110000 0.196661 0.103412           0.093249\n",
      "0.120000 0.213722 0.112425           0.101296\n",
      "0.130000 0.230572 0.121335           0.109237\n",
      "0.140000 0.247194 0.130130           0.117064\n",
      "0.150000 0.263573 0.138804           0.124769\n",
      "0.160000 0.279691 0.147347           0.132344\n",
      "0.170000 0.295534 0.155751           0.139783\n",
      "0.180000 0.311084 0.164007           0.147077\n",
      "0.190000 0.326328 0.172107           0.154221\n",
      "0.200000 0.341250 0.180043           0.161207\n",
      "0.210000 0.355835 0.187807           0.168028\n",
      "0.220000 0.370069 0.195391           0.174678\n",
      "0.230000 0.383937 0.202787           0.181150\n",
      "0.240000 0.397427 0.209988           0.187439\n",
      "0.250000 0.410524 0.216987           0.193537\n",
      "0.260000 0.423217 0.223777           0.199440\n",
      "0.270000 0.435491 0.230350           0.205141\n",
      "0.280000 0.447336 0.236701           0.210635\n",
      "0.290000 0.458740 0.242822           0.215917\n",
      "0.300000 0.469690 0.248708           0.220982\n",
      "0.310000 0.480177 0.254352           0.225825\n",
      "0.320000 0.490191 0.259749           0.230442\n",
      "0.330000 0.499720 0.264893           0.234827\n",
      "0.340000 0.508756 0.269779           0.238977\n",
      "0.350000 0.517291 0.274402           0.242888\n",
      "0.360000 0.525315 0.278758           0.246557\n",
      "0.370000 0.532820 0.282841           0.249979\n",
      "0.380000 0.539799 0.286647           0.253152\n",
      "0.390000 0.546246 0.290173           0.256073\n",
      "0.400000 0.552154 0.293415           0.258739\n",
      "0.410000 0.557517 0.296369           0.261148\n",
      "0.420000 0.562329 0.299033           0.263297\n",
      "0.430000 0.566587 0.301403           0.265184\n",
      "0.440000 0.570286 0.303477           0.266809\n",
      "0.450000 0.573421 0.305253           0.268169\n",
      "0.460000 0.575991 0.306728           0.269263\n",
      "0.470000 0.577992 0.307902           0.270090\n",
      "0.480000 0.579423 0.308772           0.270651\n",
      "0.490000 0.580283 0.309338           0.270944\n",
      "0.500000 0.580569 0.309599           0.270970\n",
      "0.510000 0.580283 0.309555           0.270728\n",
      "0.520000 0.579423 0.309204           0.270219\n",
      "0.530000 0.577992 0.308549           0.269444\n",
      "0.540000 0.575991 0.307588           0.268403\n",
      "0.550000 0.573421 0.306322           0.267099\n",
      "0.560000 0.570286 0.304753           0.265532\n",
      "0.570000 0.566587 0.302883           0.263704\n",
      "0.580000 0.562329 0.300711           0.261618\n",
      "0.590000 0.557517 0.298242           0.259275\n",
      "0.600000 0.552154 0.295476           0.256678\n",
      "0.610000 0.546246 0.292417           0.253829\n",
      "0.620000 0.539799 0.289067           0.250733\n",
      "0.630000 0.532820 0.285429           0.247391\n",
      "0.640000 0.525315 0.281507           0.243808\n",
      "0.650000 0.517291 0.277304           0.239987\n",
      "0.660000 0.508756 0.272824           0.235932\n",
      "0.670000 0.499720 0.268072           0.231648\n",
      "0.680000 0.490191 0.263052           0.227138\n",
      "0.690000 0.480177 0.257769           0.222408\n",
      "0.700000 0.469690 0.252228           0.217462\n",
      "0.710000 0.458740 0.246434           0.212306\n",
      "0.720000 0.447336 0.240392           0.206944\n",
      "0.730000 0.435491 0.234109           0.201382\n",
      "0.740000 0.423217 0.227591           0.195626\n",
      "0.750000 0.410524 0.220843           0.189681\n",
      "0.760000 0.397427 0.213873           0.183554\n",
      "0.770000 0.383937 0.206686           0.177251\n",
      "0.780000 0.370069 0.199291           0.170778\n",
      "0.790000 0.355835 0.191693           0.164141\n",
      "0.800000 0.341250 0.183901           0.157349\n",
      "0.810000 0.326328 0.175922           0.150406\n",
      "0.820000 0.311084 0.167764           0.143320\n",
      "0.830000 0.295534 0.159434           0.136099\n",
      "0.840000 0.279691 0.150941           0.128750\n",
      "0.850000 0.263573 0.142294           0.121279\n",
      "0.860000 0.247194 0.133499           0.113695\n",
      "0.870000 0.230572 0.124566           0.106005\n",
      "0.880000 0.213722 0.115505           0.098217\n",
      "0.890000 0.196661 0.106322           0.090339\n",
      "0.900000 0.179406 0.097028           0.082377\n",
      "0.910000 0.161974 0.087632           0.074342\n",
      "0.920000 0.144382 0.078142           0.066239\n",
      "0.930000 0.126647 0.068569           0.058078\n",
      "0.940000 0.108788 0.058921           0.049867\n",
      "0.950000 0.090821 0.049208           0.041613\n",
      "0.960000 0.072765 0.039439           0.033326\n",
      "0.970000 0.054636 0.029624           0.025012\n",
      "0.980000 0.036454 0.019773           0.016682\n",
      "0.990000 0.018236 0.009895           0.008341\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.21\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.019274 0.010205           0.009069\n",
      "0.020000 0.038529 0.020407           0.018122\n",
      "0.030000 0.057746 0.030597           0.027149\n",
      "0.040000 0.076906 0.040764           0.036142\n",
      "0.050000 0.095990 0.050899           0.045091\n",
      "0.060000 0.114980 0.060991           0.053989\n",
      "0.070000 0.133855 0.071030           0.062825\n",
      "0.080000 0.152599 0.081007           0.071592\n",
      "0.090000 0.171192 0.090911           0.080282\n",
      "0.100000 0.189617 0.100732           0.088885\n",
      "0.110000 0.207854 0.110461           0.097393\n",
      "0.120000 0.225886 0.120088           0.105797\n",
      "0.130000 0.243695 0.129604           0.114091\n",
      "0.140000 0.261263 0.138998           0.122265\n",
      "0.150000 0.278574 0.148262           0.130312\n",
      "0.160000 0.295610 0.157386           0.138224\n",
      "0.170000 0.312354 0.166361           0.145993\n",
      "0.180000 0.328790 0.175179           0.153611\n",
      "0.190000 0.344901 0.183829           0.161072\n",
      "0.200000 0.360672 0.192304           0.168368\n",
      "0.210000 0.376087 0.200595           0.175492\n",
      "0.220000 0.391131 0.208694           0.182437\n",
      "0.230000 0.405789 0.216593           0.189196\n",
      "0.240000 0.420047 0.224283           0.195764\n",
      "0.250000 0.433890 0.231757           0.202133\n",
      "0.260000 0.447304 0.239007           0.208297\n",
      "0.270000 0.460277 0.246026           0.214251\n",
      "0.280000 0.472797 0.252807           0.219989\n",
      "0.290000 0.484849 0.259343           0.225506\n",
      "0.300000 0.496423 0.265628           0.230795\n",
      "0.310000 0.507507 0.271654           0.235853\n",
      "0.320000 0.518090 0.277416           0.240674\n",
      "0.330000 0.528162 0.282908           0.245254\n",
      "0.340000 0.537713 0.288125           0.249588\n",
      "0.350000 0.546733 0.293061           0.253672\n",
      "0.360000 0.555213 0.297710           0.257503\n",
      "0.370000 0.563146 0.302069           0.261077\n",
      "0.380000 0.570522 0.306132           0.264391\n",
      "0.390000 0.577336 0.309895           0.267441\n",
      "0.400000 0.583580 0.313356           0.270225\n",
      "0.410000 0.589248 0.316509           0.272740\n",
      "0.420000 0.594335 0.319351           0.274984\n",
      "0.430000 0.598835 0.321880           0.276954\n",
      "0.440000 0.602744 0.324093           0.278651\n",
      "0.450000 0.606058 0.325987           0.280070\n",
      "0.460000 0.608774 0.327561           0.281213\n",
      "0.470000 0.610889 0.328812           0.282077\n",
      "0.480000 0.612402 0.329740           0.282662\n",
      "0.490000 0.613310 0.330342           0.282968\n",
      "0.500000 0.613612 0.330619           0.282994\n",
      "0.510000 0.613310 0.330569           0.282741\n",
      "0.520000 0.612402 0.330193           0.282209\n",
      "0.530000 0.610889 0.329490           0.281399\n",
      "0.540000 0.608774 0.328462           0.280312\n",
      "0.550000 0.606058 0.327109           0.278949\n",
      "0.560000 0.602744 0.325431           0.277312\n",
      "0.570000 0.598835 0.323431           0.275403\n",
      "0.580000 0.594335 0.321111           0.273224\n",
      "0.590000 0.589248 0.318472           0.270776\n",
      "0.600000 0.583580 0.315517           0.268064\n",
      "0.610000 0.577336 0.312248           0.265088\n",
      "0.620000 0.570522 0.308668           0.261854\n",
      "0.630000 0.563146 0.304782           0.258364\n",
      "0.640000 0.555213 0.300592           0.254621\n",
      "0.650000 0.546733 0.296102           0.250631\n",
      "0.660000 0.537713 0.291317           0.246396\n",
      "0.670000 0.528162 0.286241           0.241921\n",
      "0.680000 0.518090 0.280879           0.237211\n",
      "0.690000 0.507507 0.275236           0.232271\n",
      "0.700000 0.496423 0.269318           0.227105\n",
      "0.710000 0.484849 0.263129           0.221720\n",
      "0.720000 0.472797 0.256677           0.216120\n",
      "0.730000 0.460277 0.249967           0.210311\n",
      "0.740000 0.447304 0.243005           0.204299\n",
      "0.750000 0.433890 0.235799           0.198091\n",
      "0.760000 0.420047 0.228355           0.191692\n",
      "0.770000 0.405789 0.220680           0.185109\n",
      "0.780000 0.391131 0.212783           0.178348\n",
      "0.790000 0.376087 0.204670           0.171418\n",
      "0.800000 0.360672 0.196349           0.164323\n",
      "0.810000 0.344901 0.187829           0.157073\n",
      "0.820000 0.328790 0.179117           0.149673\n",
      "0.830000 0.312354 0.170223           0.142131\n",
      "0.840000 0.295610 0.161154           0.134456\n",
      "0.850000 0.278574 0.151920           0.126654\n",
      "0.860000 0.261263 0.142530           0.118734\n",
      "0.870000 0.243695 0.132992           0.110703\n",
      "0.880000 0.225886 0.123316           0.102570\n",
      "0.890000 0.207854 0.113512           0.094342\n",
      "0.900000 0.189617 0.103589           0.086028\n",
      "0.910000 0.171192 0.093557           0.077636\n",
      "0.920000 0.152599 0.083425           0.069174\n",
      "0.930000 0.133855 0.073204           0.060652\n",
      "0.940000 0.114980 0.062903           0.052076\n",
      "0.950000 0.095990 0.052533           0.043457\n",
      "0.960000 0.076906 0.042104           0.034802\n",
      "0.970000 0.057746 0.031625           0.026121\n",
      "0.980000 0.038529 0.021109           0.017420\n",
      "0.990000 0.019274 0.010563           0.008711\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.22\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.020331 0.010883           0.009448\n",
      "0.020000 0.040642 0.021762           0.018879\n",
      "0.030000 0.060913 0.032629           0.028284\n",
      "0.040000 0.081123 0.043471           0.037652\n",
      "0.050000 0.101254 0.054279           0.046975\n",
      "0.060000 0.121285 0.065040           0.056244\n",
      "0.070000 0.141196 0.075746           0.065450\n",
      "0.080000 0.160967 0.086384           0.074584\n",
      "0.090000 0.180580 0.096944           0.083636\n",
      "0.100000 0.200015 0.107417           0.092598\n",
      "0.110000 0.219252 0.117791           0.101461\n",
      "0.120000 0.238273 0.128056           0.110217\n",
      "0.130000 0.257059 0.138202           0.118857\n",
      "0.140000 0.275591 0.148218           0.127372\n",
      "0.150000 0.293851 0.158095           0.135755\n",
      "0.160000 0.311821 0.167823           0.143997\n",
      "0.170000 0.329483 0.177393           0.152090\n",
      "0.180000 0.346820 0.186793           0.160027\n",
      "0.190000 0.363815 0.196016           0.167799\n",
      "0.200000 0.380451 0.205052           0.175399\n",
      "0.210000 0.396711 0.213891           0.182820\n",
      "0.220000 0.412580 0.222525           0.190055\n",
      "0.230000 0.428042 0.230945           0.197096\n",
      "0.240000 0.443081 0.239143           0.203938\n",
      "0.250000 0.457683 0.247111           0.210572\n",
      "0.260000 0.471833 0.254840           0.216994\n",
      "0.270000 0.485518 0.262322           0.223196\n",
      "0.280000 0.498724 0.269550           0.229173\n",
      "0.290000 0.511437 0.276517           0.234920\n",
      "0.300000 0.523646 0.283216           0.240429\n",
      "0.310000 0.535337 0.289640           0.245698\n",
      "0.320000 0.546501 0.295781           0.250720\n",
      "0.330000 0.557125 0.301635           0.255490\n",
      "0.340000 0.567200 0.307195           0.260005\n",
      "0.350000 0.576714 0.312455           0.264259\n",
      "0.360000 0.585660 0.317410           0.268250\n",
      "0.370000 0.594027 0.322055           0.271972\n",
      "0.380000 0.601809 0.326385           0.275424\n",
      "0.390000 0.608996 0.330395           0.278601\n",
      "0.400000 0.615582 0.334082           0.281500\n",
      "0.410000 0.621561 0.337441           0.284120\n",
      "0.420000 0.626927 0.340470           0.286457\n",
      "0.430000 0.631673 0.343164           0.288510\n",
      "0.440000 0.635797 0.345521           0.290276\n",
      "0.450000 0.639293 0.347538           0.291755\n",
      "0.460000 0.642158 0.349213           0.292944\n",
      "0.470000 0.644389 0.350545           0.293844\n",
      "0.480000 0.645984 0.351532           0.294453\n",
      "0.490000 0.646942 0.352171           0.294771\n",
      "0.500000 0.647262 0.352464           0.294798\n",
      "0.510000 0.646942 0.352409           0.294534\n",
      "0.520000 0.645984 0.352005           0.293979\n",
      "0.530000 0.644389 0.351254           0.293135\n",
      "0.540000 0.642158 0.350156           0.292002\n",
      "0.550000 0.639293 0.348710           0.290582\n",
      "0.560000 0.635797 0.346920           0.288877\n",
      "0.570000 0.631673 0.344786           0.286887\n",
      "0.580000 0.626927 0.342310           0.284616\n",
      "0.590000 0.621561 0.339495           0.282067\n",
      "0.600000 0.615582 0.336342           0.279240\n",
      "0.610000 0.608996 0.332855           0.276141\n",
      "0.620000 0.601809 0.329038           0.272771\n",
      "0.630000 0.594027 0.324892           0.269135\n",
      "0.640000 0.585660 0.320424           0.265236\n",
      "0.650000 0.576714 0.315636           0.261079\n",
      "0.660000 0.567200 0.310533           0.256667\n",
      "0.670000 0.557125 0.305120           0.252005\n",
      "0.680000 0.546501 0.299403           0.247098\n",
      "0.690000 0.535337 0.293386           0.241952\n",
      "0.700000 0.523646 0.287075           0.236571\n",
      "0.710000 0.511437 0.280477           0.230960\n",
      "0.720000 0.498724 0.273597           0.225127\n",
      "0.730000 0.485518 0.266443           0.219075\n",
      "0.740000 0.471833 0.259021           0.212813\n",
      "0.750000 0.457683 0.251338           0.206345\n",
      "0.760000 0.443081 0.243402           0.199679\n",
      "0.770000 0.428042 0.235220           0.192822\n",
      "0.780000 0.412580 0.226801           0.185779\n",
      "0.790000 0.396711 0.218152           0.178560\n",
      "0.800000 0.380451 0.209281           0.171169\n",
      "0.810000 0.363815 0.200199           0.163616\n",
      "0.820000 0.346820 0.190912           0.155908\n",
      "0.830000 0.329483 0.181431           0.148052\n",
      "0.840000 0.311821 0.171764           0.140057\n",
      "0.850000 0.293851 0.161921           0.131930\n",
      "0.860000 0.275591 0.151911           0.123679\n",
      "0.870000 0.257059 0.141745           0.115314\n",
      "0.880000 0.238273 0.131431           0.106841\n",
      "0.890000 0.219252 0.120981           0.098271\n",
      "0.900000 0.200015 0.110405           0.089610\n",
      "0.910000 0.180580 0.099711           0.080869\n",
      "0.920000 0.160967 0.088913           0.072055\n",
      "0.930000 0.141196 0.078019           0.063177\n",
      "0.940000 0.121285 0.067040           0.054245\n",
      "0.950000 0.101254 0.055987           0.045267\n",
      "0.960000 0.081123 0.044872           0.036251\n",
      "0.970000 0.060913 0.033705           0.027208\n",
      "0.980000 0.040642 0.022496           0.018146\n",
      "0.990000 0.020331 0.011258           0.009073\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.23\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.021408 0.011588           0.009820\n",
      "0.020000 0.042795 0.023173           0.019622\n",
      "0.030000 0.064139 0.034743           0.029396\n",
      "0.040000 0.085421 0.046288           0.039133\n",
      "0.050000 0.106618 0.057795           0.048823\n",
      "0.060000 0.127710 0.069253           0.058457\n",
      "0.070000 0.148675 0.080651           0.068024\n",
      "0.080000 0.169494 0.091977           0.077517\n",
      "0.090000 0.190146 0.103221           0.086925\n",
      "0.100000 0.210610 0.114371           0.096240\n",
      "0.110000 0.230867 0.125415           0.105451\n",
      "0.120000 0.250895 0.136344           0.114551\n",
      "0.130000 0.270676 0.147145           0.123531\n",
      "0.140000 0.290190 0.157809           0.132381\n",
      "0.150000 0.309417 0.168324           0.141093\n",
      "0.160000 0.328339 0.178680           0.149659\n",
      "0.170000 0.346937 0.188867           0.158070\n",
      "0.180000 0.365193 0.198875           0.166318\n",
      "0.190000 0.383088 0.208692           0.174395\n",
      "0.200000 0.400605 0.218311           0.182294\n",
      "0.210000 0.417727 0.227720           0.190006\n",
      "0.220000 0.434436 0.236911           0.197525\n",
      "0.230000 0.450717 0.245874           0.204843\n",
      "0.240000 0.466553 0.254600           0.211953\n",
      "0.250000 0.481928 0.263080           0.218848\n",
      "0.260000 0.496828 0.271307           0.225521\n",
      "0.270000 0.511238 0.279271           0.231967\n",
      "0.280000 0.525143 0.286964           0.238179\n",
      "0.290000 0.538530 0.294379           0.244150\n",
      "0.300000 0.551385 0.301509           0.249876\n",
      "0.310000 0.563696 0.308345           0.255351\n",
      "0.320000 0.575451 0.314881           0.260570\n",
      "0.330000 0.586638 0.321111           0.265527\n",
      "0.340000 0.597246 0.327027           0.270219\n",
      "0.350000 0.607265 0.332625           0.274640\n",
      "0.360000 0.616684 0.337898           0.278787\n",
      "0.370000 0.625495 0.342840           0.282655\n",
      "0.380000 0.633689 0.347447           0.286242\n",
      "0.390000 0.641257 0.351714           0.289543\n",
      "0.400000 0.648192 0.355636           0.292556\n",
      "0.410000 0.654488 0.359210           0.295278\n",
      "0.420000 0.660137 0.362431           0.297706\n",
      "0.430000 0.665136 0.365296           0.299839\n",
      "0.440000 0.669477 0.367803           0.301674\n",
      "0.450000 0.673159 0.369948           0.303211\n",
      "0.460000 0.676175 0.371729           0.304446\n",
      "0.470000 0.678525 0.373144           0.305381\n",
      "0.480000 0.680205 0.374191           0.306013\n",
      "0.490000 0.681213 0.374870           0.306343\n",
      "0.500000 0.681550 0.375179           0.306371\n",
      "0.510000 0.681213 0.375118           0.306096\n",
      "0.520000 0.680205 0.374686           0.305519\n",
      "0.530000 0.678525 0.373884           0.304641\n",
      "0.540000 0.676175 0.372712           0.303464\n",
      "0.550000 0.673159 0.371171           0.301987\n",
      "0.560000 0.669477 0.369263           0.300214\n",
      "0.570000 0.665136 0.366989           0.298146\n",
      "0.580000 0.660137 0.364351           0.295786\n",
      "0.590000 0.654488 0.361352           0.293136\n",
      "0.600000 0.648192 0.357994           0.290198\n",
      "0.610000 0.641257 0.354281           0.286976\n",
      "0.620000 0.633689 0.350215           0.283474\n",
      "0.630000 0.625495 0.345801           0.279695\n",
      "0.640000 0.616684 0.341042           0.275642\n",
      "0.650000 0.607265 0.335944           0.271321\n",
      "0.660000 0.597246 0.330510           0.266736\n",
      "0.670000 0.586638 0.324747           0.261891\n",
      "0.680000 0.575451 0.318660           0.256791\n",
      "0.690000 0.563696 0.312254           0.251443\n",
      "0.700000 0.551385 0.305535           0.245850\n",
      "0.710000 0.538530 0.298511           0.240019\n",
      "0.720000 0.525143 0.291187           0.233956\n",
      "0.730000 0.511238 0.283571           0.227667\n",
      "0.740000 0.496828 0.275670           0.221159\n",
      "0.750000 0.481928 0.267491           0.214437\n",
      "0.760000 0.466553 0.259043           0.207510\n",
      "0.770000 0.450717 0.250334           0.200383\n",
      "0.780000 0.434436 0.241372           0.193064\n",
      "0.790000 0.417727 0.232166           0.185561\n",
      "0.800000 0.400605 0.222724           0.177880\n",
      "0.810000 0.383088 0.213057           0.170031\n",
      "0.820000 0.365193 0.203172           0.162020\n",
      "0.830000 0.346937 0.193081           0.153856\n",
      "0.840000 0.328339 0.182792           0.145547\n",
      "0.850000 0.309417 0.172316           0.137101\n",
      "0.860000 0.290190 0.161662           0.128527\n",
      "0.870000 0.270676 0.150842           0.119834\n",
      "0.880000 0.250895 0.139866           0.111029\n",
      "0.890000 0.230867 0.128744           0.102122\n",
      "0.900000 0.210610 0.117488           0.093122\n",
      "0.910000 0.190146 0.106108           0.084038\n",
      "0.920000 0.169494 0.094616           0.074878\n",
      "0.930000 0.148675 0.083023           0.065653\n",
      "0.940000 0.127710 0.071339           0.056370\n",
      "0.950000 0.106618 0.059578           0.047040\n",
      "0.960000 0.085421 0.047749           0.037672\n",
      "0.970000 0.064139 0.035865           0.028274\n",
      "0.980000 0.042795 0.023938           0.018857\n",
      "0.990000 0.021408 0.011979           0.009429\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.24\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.022506 0.012322           0.010184\n",
      "0.020000 0.044990 0.024640           0.020350\n",
      "0.030000 0.067430 0.036943           0.030486\n",
      "0.040000 0.089803 0.049219           0.040584\n",
      "0.050000 0.112087 0.061454           0.050633\n",
      "0.060000 0.134261 0.073637           0.060623\n",
      "0.070000 0.156302 0.085756           0.070546\n",
      "0.080000 0.178189 0.097799           0.080390\n",
      "0.090000 0.199900 0.109754           0.090146\n",
      "0.100000 0.221414 0.121608           0.099806\n",
      "0.110000 0.242709 0.133350           0.109359\n",
      "0.120000 0.263765 0.144969           0.118796\n",
      "0.130000 0.284561 0.156453           0.128108\n",
      "0.140000 0.305075 0.167790           0.137285\n",
      "0.150000 0.325289 0.178969           0.146320\n",
      "0.160000 0.345181 0.189979           0.155203\n",
      "0.170000 0.364733 0.200808           0.163925\n",
      "0.180000 0.383925 0.211447           0.172479\n",
      "0.190000 0.402738 0.221883           0.180855\n",
      "0.200000 0.421154 0.232108           0.189046\n",
      "0.210000 0.439154 0.242110           0.197044\n",
      "0.220000 0.456721 0.251880           0.204841\n",
      "0.230000 0.473837 0.261408           0.212429\n",
      "0.240000 0.490485 0.270683           0.219802\n",
      "0.250000 0.506649 0.279697           0.226952\n",
      "0.260000 0.522313 0.288441           0.233872\n",
      "0.270000 0.537462 0.296906           0.240556\n",
      "0.280000 0.552081 0.305083           0.246997\n",
      "0.290000 0.566154 0.312965           0.253190\n",
      "0.300000 0.579669 0.320542           0.259127\n",
      "0.310000 0.592612 0.327807           0.264804\n",
      "0.320000 0.604970 0.334754           0.270216\n",
      "0.330000 0.616730 0.341374           0.275356\n",
      "0.340000 0.627883 0.347662           0.280221\n",
      "0.350000 0.638415 0.353610           0.284805\n",
      "0.360000 0.648318 0.359213           0.289105\n",
      "0.370000 0.657581 0.364464           0.293116\n",
      "0.380000 0.666194 0.369359           0.296835\n",
      "0.390000 0.674151 0.373893           0.300258\n",
      "0.400000 0.681442 0.378060           0.303382\n",
      "0.410000 0.688060 0.381856           0.306204\n",
      "0.420000 0.694000 0.385278           0.308722\n",
      "0.430000 0.699254 0.388321           0.310933\n",
      "0.440000 0.703819 0.390983           0.312836\n",
      "0.450000 0.707689 0.393261           0.314428\n",
      "0.460000 0.710860 0.395151           0.315709\n",
      "0.470000 0.713330 0.396653           0.316678\n",
      "0.480000 0.715096 0.397764           0.317333\n",
      "0.490000 0.716157 0.398482           0.317674\n",
      "0.500000 0.716510 0.398808           0.317702\n",
      "0.510000 0.716157 0.398740           0.317417\n",
      "0.520000 0.715096 0.398278           0.316818\n",
      "0.530000 0.713330 0.397423           0.315907\n",
      "0.540000 0.710860 0.396175           0.314686\n",
      "0.550000 0.707689 0.394535           0.313154\n",
      "0.560000 0.703819 0.392504           0.311315\n",
      "0.570000 0.699254 0.390084           0.309170\n",
      "0.580000 0.694000 0.387278           0.306722\n",
      "0.590000 0.688060 0.384087           0.303973\n",
      "0.600000 0.681442 0.380515           0.300926\n",
      "0.610000 0.674151 0.376566           0.297585\n",
      "0.620000 0.666194 0.372242           0.293953\n",
      "0.630000 0.657581 0.367547           0.290033\n",
      "0.640000 0.648318 0.362487           0.285831\n",
      "0.650000 0.638415 0.357066           0.281350\n",
      "0.660000 0.627883 0.351288           0.276594\n",
      "0.670000 0.616730 0.345161           0.271570\n",
      "0.680000 0.604970 0.338688           0.266281\n",
      "0.690000 0.592612 0.331877           0.260734\n",
      "0.700000 0.579669 0.324734           0.254935\n",
      "0.710000 0.566154 0.317266           0.248888\n",
      "0.720000 0.552081 0.309480           0.242601\n",
      "0.730000 0.537462 0.301383           0.236079\n",
      "0.740000 0.522313 0.292984           0.229330\n",
      "0.750000 0.506649 0.284290           0.222359\n",
      "0.760000 0.490485 0.275310           0.215175\n",
      "0.770000 0.473837 0.266052           0.207785\n",
      "0.780000 0.456721 0.256525           0.200195\n",
      "0.790000 0.439154 0.246739           0.192415\n",
      "0.800000 0.421154 0.236704           0.184451\n",
      "0.810000 0.402738 0.226428           0.176311\n",
      "0.820000 0.383925 0.215921           0.168004\n",
      "0.830000 0.364733 0.205195           0.159538\n",
      "0.840000 0.345181 0.194259           0.150922\n",
      "0.850000 0.325289 0.183125           0.142164\n",
      "0.860000 0.305075 0.171802           0.133273\n",
      "0.870000 0.284561 0.160302           0.124258\n",
      "0.880000 0.263765 0.148637           0.115128\n",
      "0.890000 0.242709 0.136817           0.105893\n",
      "0.900000 0.221414 0.124854           0.096560\n",
      "0.910000 0.199900 0.112760           0.087140\n",
      "0.920000 0.178189 0.100546           0.077642\n",
      "0.930000 0.156302 0.088226           0.068076\n",
      "0.940000 0.134261 0.075810           0.058451\n",
      "0.950000 0.112087 0.063311           0.048776\n",
      "0.960000 0.089803 0.050741           0.039062\n",
      "0.970000 0.067430 0.038112           0.029317\n",
      "0.980000 0.044990 0.025438           0.019553\n",
      "0.990000 0.022506 0.012729           0.009777\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.25\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.023626 0.013086           0.010540\n",
      "0.020000 0.047230 0.026169           0.021061\n",
      "0.030000 0.070786 0.039234           0.031552\n",
      "0.040000 0.094273 0.052270           0.042003\n",
      "0.050000 0.117667 0.065264           0.052403\n",
      "0.060000 0.140944 0.078202           0.062743\n",
      "0.070000 0.164083 0.091071           0.073011\n",
      "0.080000 0.187059 0.103860           0.083200\n",
      "0.090000 0.209851 0.116554           0.093297\n",
      "0.100000 0.232436 0.129142           0.103294\n",
      "0.110000 0.254791 0.141611           0.113180\n",
      "0.120000 0.276895 0.153948           0.122947\n",
      "0.130000 0.298726 0.166142           0.132584\n",
      "0.140000 0.320262 0.178180           0.142082\n",
      "0.150000 0.341482 0.190050           0.151432\n",
      "0.160000 0.362365 0.201740           0.160625\n",
      "0.170000 0.382890 0.213238           0.169652\n",
      "0.180000 0.403037 0.224533           0.178504\n",
      "0.190000 0.422787 0.235615           0.187172\n",
      "0.200000 0.442119 0.246470           0.195649\n",
      "0.210000 0.461015 0.257089           0.203926\n",
      "0.220000 0.479456 0.267462           0.211995\n",
      "0.230000 0.497424 0.277577           0.219848\n",
      "0.240000 0.514901 0.287424           0.227478\n",
      "0.250000 0.531870 0.296994           0.234877\n",
      "0.260000 0.548314 0.306276           0.242038\n",
      "0.270000 0.564217 0.315262           0.248955\n",
      "0.280000 0.579563 0.323943           0.255621\n",
      "0.290000 0.594337 0.332309           0.262029\n",
      "0.300000 0.608525 0.340352           0.268173\n",
      "0.310000 0.622112 0.348064           0.274048\n",
      "0.320000 0.635085 0.355437           0.279648\n",
      "0.330000 0.647431 0.362464           0.284967\n",
      "0.340000 0.659139 0.369137           0.290001\n",
      "0.350000 0.670196 0.375450           0.294745\n",
      "0.360000 0.680591 0.381397           0.299195\n",
      "0.370000 0.690315 0.386970           0.303345\n",
      "0.380000 0.699358 0.392165           0.307193\n",
      "0.390000 0.707710 0.396975           0.310735\n",
      "0.400000 0.715364 0.401397           0.313967\n",
      "0.410000 0.722312 0.405425           0.316887\n",
      "0.420000 0.728547 0.409055           0.319492\n",
      "0.430000 0.734063 0.412283           0.321780\n",
      "0.440000 0.738855 0.415106           0.323749\n",
      "0.450000 0.742918 0.417521           0.325396\n",
      "0.460000 0.746247 0.419526           0.326721\n",
      "0.470000 0.748840 0.421117           0.327723\n",
      "0.480000 0.750694 0.422293           0.328401\n",
      "0.490000 0.751807 0.423053           0.328754\n",
      "0.500000 0.752178 0.423396           0.328782\n",
      "0.510000 0.751807 0.423321           0.328486\n",
      "0.520000 0.750694 0.422828           0.327866\n",
      "0.530000 0.748840 0.421917           0.326923\n",
      "0.540000 0.746247 0.420589           0.325658\n",
      "0.550000 0.742918 0.418845           0.324073\n",
      "0.560000 0.738855 0.416686           0.322169\n",
      "0.570000 0.734063 0.414115           0.319949\n",
      "0.580000 0.728547 0.411133           0.317414\n",
      "0.590000 0.722312 0.407743           0.314569\n",
      "0.600000 0.715364 0.403948           0.311416\n",
      "0.610000 0.707710 0.399753           0.307957\n",
      "0.620000 0.699358 0.395160           0.304198\n",
      "0.630000 0.690315 0.390174           0.300141\n",
      "0.640000 0.680591 0.384799           0.295792\n",
      "0.650000 0.670196 0.379042           0.291154\n",
      "0.660000 0.659139 0.372906           0.286232\n",
      "0.670000 0.647431 0.366399           0.281032\n",
      "0.680000 0.635085 0.359526           0.275559\n",
      "0.690000 0.622112 0.352293           0.269819\n",
      "0.700000 0.608525 0.344709           0.263816\n",
      "0.710000 0.594337 0.336779           0.257559\n",
      "0.720000 0.579563 0.328512           0.251052\n",
      "0.730000 0.564217 0.319915           0.244302\n",
      "0.740000 0.548314 0.310997           0.237317\n",
      "0.750000 0.531870 0.301766           0.230104\n",
      "0.760000 0.514901 0.292232           0.222670\n",
      "0.770000 0.497424 0.282403           0.215021\n",
      "0.780000 0.479456 0.272289           0.207167\n",
      "0.790000 0.461015 0.261900           0.199115\n",
      "0.800000 0.442119 0.251246           0.190873\n",
      "0.810000 0.422787 0.240337           0.182450\n",
      "0.820000 0.403037 0.229184           0.173853\n",
      "0.830000 0.382890 0.217797           0.165093\n",
      "0.840000 0.362365 0.206188           0.156176\n",
      "0.850000 0.341482 0.194369           0.147113\n",
      "0.860000 0.320262 0.182349           0.137912\n",
      "0.870000 0.298726 0.170142           0.128584\n",
      "0.880000 0.276895 0.157760           0.119136\n",
      "0.890000 0.254791 0.145213           0.109578\n",
      "0.900000 0.232436 0.132515           0.099921\n",
      "0.910000 0.209851 0.119678           0.090173\n",
      "0.920000 0.187059 0.106715           0.080344\n",
      "0.930000 0.164083 0.093637           0.070445\n",
      "0.940000 0.140944 0.080459           0.060485\n",
      "0.950000 0.117667 0.067193           0.050473\n",
      "0.960000 0.094273 0.053852           0.040421\n",
      "0.970000 0.070786 0.040449           0.030337\n",
      "0.980000 0.047230 0.026997           0.020233\n",
      "0.990000 0.023626 0.013510           0.010117\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.26\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.024770 0.013882           0.010888\n",
      "0.020000 0.049516 0.027760           0.021756\n",
      "0.030000 0.074213 0.041620           0.032593\n",
      "0.040000 0.098836 0.055448           0.043388\n",
      "0.050000 0.123362 0.069231           0.054131\n",
      "0.060000 0.147767 0.082955           0.064812\n",
      "0.070000 0.172025 0.096606           0.075419\n",
      "0.080000 0.196114 0.110171           0.085943\n",
      "0.090000 0.220009 0.123636           0.096374\n",
      "0.100000 0.243687 0.136987           0.106700\n",
      "0.110000 0.267125 0.150213           0.116912\n",
      "0.120000 0.290299 0.163298           0.127000\n",
      "0.130000 0.313186 0.176231           0.136955\n",
      "0.140000 0.335765 0.188999           0.146766\n",
      "0.150000 0.358012 0.201588           0.156424\n",
      "0.160000 0.379905 0.213986           0.165920\n",
      "0.170000 0.401424 0.226181           0.175244\n",
      "0.180000 0.422547 0.238160           0.184387\n",
      "0.190000 0.443253 0.249912           0.193341\n",
      "0.200000 0.463521 0.261424           0.202097\n",
      "0.210000 0.483331 0.272686           0.210646\n",
      "0.220000 0.502665 0.283685           0.218980\n",
      "0.230000 0.521503 0.294411           0.227092\n",
      "0.240000 0.539826 0.304854           0.234972\n",
      "0.250000 0.557616 0.315001           0.242615\n",
      "0.260000 0.574856 0.324844           0.250012\n",
      "0.270000 0.591529 0.334373           0.257156\n",
      "0.280000 0.607618 0.343577           0.264041\n",
      "0.290000 0.623107 0.352448           0.270660\n",
      "0.300000 0.637982 0.360976           0.277006\n",
      "0.310000 0.652226 0.369152           0.283074\n",
      "0.320000 0.665827 0.376970           0.288857\n",
      "0.330000 0.678771 0.384420           0.294352\n",
      "0.340000 0.691045 0.391495           0.299551\n",
      "0.350000 0.702638 0.398187           0.304450\n",
      "0.360000 0.713536 0.404491           0.309046\n",
      "0.370000 0.723731 0.410399           0.313332\n",
      "0.380000 0.733211 0.415905           0.317306\n",
      "0.390000 0.741968 0.421004           0.320964\n",
      "0.400000 0.749992 0.425690           0.324302\n",
      "0.410000 0.757277 0.429959           0.327318\n",
      "0.420000 0.763814 0.433805           0.330008\n",
      "0.430000 0.769597 0.437226           0.332371\n",
      "0.440000 0.774620 0.440217           0.334404\n",
      "0.450000 0.778880 0.442775           0.336105\n",
      "0.460000 0.782370 0.444898           0.337473\n",
      "0.470000 0.785089 0.446582           0.338507\n",
      "0.480000 0.787032 0.447826           0.339206\n",
      "0.490000 0.788199 0.448629           0.339570\n",
      "0.500000 0.788589 0.448990           0.339599\n",
      "0.510000 0.788199 0.448907           0.339292\n",
      "0.520000 0.787032 0.448381           0.338651\n",
      "0.530000 0.785089 0.447412           0.337677\n",
      "0.540000 0.782370 0.446001           0.336369\n",
      "0.550000 0.778880 0.444148           0.334731\n",
      "0.560000 0.774620 0.441856           0.332764\n",
      "0.570000 0.769597 0.439126           0.330471\n",
      "0.580000 0.763814 0.435961           0.327853\n",
      "0.590000 0.757277 0.432363           0.324913\n",
      "0.600000 0.749992 0.428337           0.321655\n",
      "0.610000 0.741968 0.423885           0.318083\n",
      "0.620000 0.733211 0.419012           0.314199\n",
      "0.630000 0.723731 0.413722           0.310009\n",
      "0.640000 0.713536 0.408020           0.305516\n",
      "0.650000 0.702638 0.401913           0.300725\n",
      "0.660000 0.691045 0.395404           0.295641\n",
      "0.670000 0.678771 0.388502           0.290270\n",
      "0.680000 0.665827 0.381211           0.284616\n",
      "0.690000 0.652226 0.373540           0.278686\n",
      "0.700000 0.637982 0.365495           0.272486\n",
      "0.710000 0.623107 0.357085           0.266022\n",
      "0.720000 0.607618 0.348317           0.259301\n",
      "0.730000 0.591529 0.339199           0.252330\n",
      "0.740000 0.574856 0.329741           0.245115\n",
      "0.750000 0.557616 0.319952           0.237664\n",
      "0.760000 0.539826 0.309841           0.229985\n",
      "0.770000 0.521503 0.299418           0.222085\n",
      "0.780000 0.502665 0.288693           0.213972\n",
      "0.790000 0.483331 0.277676           0.205656\n",
      "0.800000 0.463521 0.266378           0.197143\n",
      "0.810000 0.443253 0.254810           0.188442\n",
      "0.820000 0.422547 0.242984           0.179563\n",
      "0.830000 0.401424 0.230910           0.170514\n",
      "0.840000 0.379905 0.218601           0.161305\n",
      "0.850000 0.358012 0.206068           0.151944\n",
      "0.860000 0.335765 0.193324           0.142441\n",
      "0.870000 0.313186 0.180381           0.132805\n",
      "0.880000 0.290299 0.167252           0.123047\n",
      "0.890000 0.267125 0.153949           0.113175\n",
      "0.900000 0.243687 0.140486           0.103201\n",
      "0.910000 0.220009 0.126876           0.093133\n",
      "0.920000 0.196114 0.113132           0.082982\n",
      "0.930000 0.172025 0.099268           0.072757\n",
      "0.940000 0.147767 0.085297           0.062470\n",
      "0.950000 0.123362 0.071232           0.052130\n",
      "0.960000 0.098836 0.057089           0.041747\n",
      "0.970000 0.074213 0.042880           0.031333\n",
      "0.980000 0.049516 0.028619           0.020897\n",
      "0.990000 0.024770 0.014321           0.010449\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.27\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.025938 0.014711           0.011227\n",
      "0.020000 0.051851 0.029418           0.022433\n",
      "0.030000 0.077713 0.044105           0.033608\n",
      "0.040000 0.103497 0.058758           0.044739\n",
      "0.050000 0.129180 0.073363           0.055817\n",
      "0.060000 0.154735 0.087906           0.066830\n",
      "0.070000 0.180138 0.102371           0.077767\n",
      "0.080000 0.205362 0.116744           0.088618\n",
      "0.090000 0.230385 0.131011           0.099373\n",
      "0.100000 0.255179 0.145159           0.110021\n",
      "0.110000 0.279722 0.159172           0.120551\n",
      "0.120000 0.303989 0.173036           0.130953\n",
      "0.130000 0.327956 0.186739           0.141217\n",
      "0.140000 0.351599 0.200266           0.151333\n",
      "0.150000 0.374895 0.213604           0.161291\n",
      "0.160000 0.397821 0.226740           0.171082\n",
      "0.170000 0.420355 0.239660           0.180695\n",
      "0.180000 0.442474 0.252351           0.190123\n",
      "0.190000 0.464156 0.264801           0.199355\n",
      "0.200000 0.485380 0.276997           0.208383\n",
      "0.210000 0.506125 0.288927           0.217197\n",
      "0.220000 0.526370 0.300580           0.225790\n",
      "0.230000 0.546096 0.311943           0.234154\n",
      "0.240000 0.565283 0.323004           0.242279\n",
      "0.250000 0.583913 0.333754           0.250159\n",
      "0.260000 0.601966 0.344181           0.257785\n",
      "0.270000 0.619425 0.354274           0.265151\n",
      "0.280000 0.636272 0.364023           0.272249\n",
      "0.290000 0.652492 0.373419           0.279073\n",
      "0.300000 0.668068 0.382452           0.285616\n",
      "0.310000 0.682984 0.391112           0.291872\n",
      "0.320000 0.697227 0.399392           0.297835\n",
      "0.330000 0.710781 0.407282           0.303500\n",
      "0.340000 0.723634 0.414774           0.308860\n",
      "0.350000 0.735773 0.421862           0.313911\n",
      "0.360000 0.747186 0.428537           0.318648\n",
      "0.370000 0.757861 0.434793           0.323068\n",
      "0.380000 0.767788 0.440624           0.327165\n",
      "0.390000 0.776958 0.446022           0.330936\n",
      "0.400000 0.785361 0.450984           0.334377\n",
      "0.410000 0.792989 0.455503           0.337486\n",
      "0.420000 0.799834 0.459575           0.340259\n",
      "0.430000 0.805890 0.463196           0.342694\n",
      "0.440000 0.811150 0.466361           0.344789\n",
      "0.450000 0.815611 0.469068           0.346543\n",
      "0.460000 0.819266 0.471313           0.347953\n",
      "0.470000 0.822112 0.473094           0.349018\n",
      "0.480000 0.824148 0.474409           0.349739\n",
      "0.490000 0.825370 0.475257           0.350113\n",
      "0.500000 0.825777 0.475635           0.350142\n",
      "0.510000 0.825370 0.475544           0.349825\n",
      "0.520000 0.824148 0.474984           0.349164\n",
      "0.530000 0.822112 0.473954           0.348158\n",
      "0.540000 0.819266 0.472456           0.346810\n",
      "0.550000 0.815611 0.470490           0.345121\n",
      "0.560000 0.811150 0.468058           0.343092\n",
      "0.570000 0.805890 0.465163           0.340726\n",
      "0.580000 0.799834 0.461807           0.338027\n",
      "0.590000 0.792989 0.457993           0.334995\n",
      "0.600000 0.785361 0.453725           0.331636\n",
      "0.610000 0.776958 0.449006           0.327952\n",
      "0.620000 0.767788 0.443841           0.323947\n",
      "0.630000 0.757861 0.438235           0.319626\n",
      "0.640000 0.747186 0.432192           0.314993\n",
      "0.650000 0.735773 0.425720           0.310053\n",
      "0.660000 0.723634 0.418823           0.304811\n",
      "0.670000 0.710781 0.411509           0.299272\n",
      "0.680000 0.697227 0.403784           0.293443\n",
      "0.690000 0.682984 0.395656           0.287329\n",
      "0.700000 0.668068 0.387132           0.280936\n",
      "0.710000 0.652492 0.378221           0.274271\n",
      "0.720000 0.636272 0.368931           0.267341\n",
      "0.730000 0.619425 0.359272           0.260153\n",
      "0.740000 0.601966 0.349252           0.252714\n",
      "0.750000 0.583913 0.338881           0.245032\n",
      "0.760000 0.565283 0.328169           0.237114\n",
      "0.770000 0.546096 0.317127           0.228969\n",
      "0.780000 0.526370 0.305766           0.220604\n",
      "0.790000 0.506125 0.294095           0.212029\n",
      "0.800000 0.485380 0.282127           0.203252\n",
      "0.810000 0.464156 0.269874           0.194282\n",
      "0.820000 0.442474 0.257346           0.185127\n",
      "0.830000 0.420355 0.244557           0.175798\n",
      "0.840000 0.397821 0.231519           0.166303\n",
      "0.850000 0.374895 0.218244           0.156651\n",
      "0.860000 0.351599 0.204745           0.146854\n",
      "0.870000 0.327956 0.191036           0.136919\n",
      "0.880000 0.303989 0.177130           0.126858\n",
      "0.890000 0.279722 0.163041           0.116681\n",
      "0.900000 0.255179 0.148782           0.106397\n",
      "0.910000 0.230385 0.134367           0.096017\n",
      "0.920000 0.205362 0.119811           0.085551\n",
      "0.930000 0.180138 0.105127           0.075010\n",
      "0.940000 0.154735 0.090331           0.064404\n",
      "0.950000 0.129180 0.075436           0.053744\n",
      "0.960000 0.103497 0.060457           0.043040\n",
      "0.970000 0.077713 0.045410           0.032303\n",
      "0.980000 0.051851 0.030307           0.021544\n",
      "0.990000 0.025938 0.015166           0.010772\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.28\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.027132 0.015575           0.011557\n",
      "0.020000 0.054237 0.031145           0.023093\n",
      "0.030000 0.081289 0.046694           0.034595\n",
      "0.040000 0.108260 0.062207           0.046054\n",
      "0.050000 0.135125 0.077668           0.057457\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.060000 0.161856 0.093063           0.068793\n",
      "0.070000 0.188428 0.108376           0.080052\n",
      "0.080000 0.214814 0.123591           0.091222\n",
      "0.090000 0.240987 0.138694           0.102293\n",
      "0.100000 0.266923 0.153670           0.113253\n",
      "0.110000 0.292595 0.168504           0.124092\n",
      "0.120000 0.317979 0.183180           0.134799\n",
      "0.130000 0.343049 0.197684           0.145364\n",
      "0.140000 0.367780 0.212003           0.155777\n",
      "0.150000 0.392148 0.226121           0.166028\n",
      "0.160000 0.416130 0.240024           0.176105\n",
      "0.170000 0.439700 0.253699           0.186001\n",
      "0.180000 0.462837 0.267132           0.195705\n",
      "0.190000 0.485517 0.280309           0.205208\n",
      "0.200000 0.507718 0.293218           0.214500\n",
      "0.210000 0.529418 0.305844           0.223573\n",
      "0.220000 0.550595 0.318177           0.232418\n",
      "0.230000 0.571229 0.330202           0.241026\n",
      "0.240000 0.591299 0.341909           0.249390\n",
      "0.250000 0.610785 0.353285           0.257500\n",
      "0.260000 0.629669 0.364319           0.265350\n",
      "0.270000 0.647932 0.375000           0.272932\n",
      "0.280000 0.665555 0.385317           0.280238\n",
      "0.290000 0.682521 0.395260           0.287261\n",
      "0.300000 0.698814 0.404818           0.293996\n",
      "0.310000 0.714417 0.413982           0.300435\n",
      "0.320000 0.729314 0.422742           0.306572\n",
      "0.330000 0.743493 0.431091           0.312402\n",
      "0.340000 0.756937 0.439018           0.317919\n",
      "0.350000 0.769635 0.446517           0.323118\n",
      "0.360000 0.781572 0.453579           0.327993\n",
      "0.370000 0.792739 0.460197           0.332542\n",
      "0.380000 0.803123 0.466365           0.336758\n",
      "0.390000 0.812715 0.472076           0.340639\n",
      "0.400000 0.821505 0.477324           0.344181\n",
      "0.410000 0.829483 0.482104           0.347380\n",
      "0.420000 0.836644 0.486410           0.350234\n",
      "0.430000 0.842978 0.490239           0.352740\n",
      "0.440000 0.848481 0.493585           0.354896\n",
      "0.450000 0.853146 0.496447           0.356700\n",
      "0.460000 0.856970 0.498820           0.358150\n",
      "0.470000 0.859948 0.500701           0.359246\n",
      "0.480000 0.862077 0.502089           0.359987\n",
      "0.490000 0.863355 0.502983           0.360372\n",
      "0.500000 0.863781 0.503380           0.360401\n",
      "0.510000 0.863355 0.503280           0.360075\n",
      "0.520000 0.862077 0.502683           0.359393\n",
      "0.530000 0.859948 0.501590           0.358358\n",
      "0.540000 0.856970 0.500001           0.356969\n",
      "0.550000 0.853146 0.497917           0.355229\n",
      "0.560000 0.848481 0.495340           0.353141\n",
      "0.570000 0.842978 0.492273           0.350705\n",
      "0.580000 0.836644 0.488718           0.347926\n",
      "0.590000 0.829483 0.484678           0.344805\n",
      "0.600000 0.821505 0.480158           0.341347\n",
      "0.610000 0.812715 0.475161           0.337554\n",
      "0.620000 0.803123 0.469692           0.333432\n",
      "0.630000 0.792739 0.463756           0.328983\n",
      "0.640000 0.781572 0.457358           0.324214\n",
      "0.650000 0.769635 0.450506           0.319129\n",
      "0.660000 0.756937 0.443204           0.313733\n",
      "0.670000 0.743493 0.435461           0.308032\n",
      "0.680000 0.729314 0.427283           0.302031\n",
      "0.690000 0.714417 0.418679           0.295737\n",
      "0.700000 0.698814 0.409657           0.289157\n",
      "0.710000 0.682521 0.400224           0.282296\n",
      "0.720000 0.665555 0.390392           0.275163\n",
      "0.730000 0.647932 0.380168           0.267764\n",
      "0.740000 0.629669 0.369562           0.260107\n",
      "0.750000 0.610785 0.358586           0.252200\n",
      "0.760000 0.591299 0.347249           0.244050\n",
      "0.770000 0.571229 0.335563           0.235666\n",
      "0.780000 0.550595 0.323538           0.227057\n",
      "0.790000 0.529418 0.311187           0.218230\n",
      "0.800000 0.507718 0.298522           0.209196\n",
      "0.810000 0.485517 0.285554           0.199963\n",
      "0.820000 0.462837 0.272297           0.190540\n",
      "0.830000 0.439700 0.258763           0.180938\n",
      "0.840000 0.416130 0.244965           0.171165\n",
      "0.850000 0.392148 0.230918           0.161231\n",
      "0.860000 0.367780 0.216634           0.151146\n",
      "0.870000 0.343049 0.202127           0.140921\n",
      "0.880000 0.317979 0.187413           0.130566\n",
      "0.890000 0.292595 0.172504           0.120091\n",
      "0.900000 0.266923 0.157416           0.109507\n",
      "0.910000 0.240987 0.142164           0.098823\n",
      "0.920000 0.214814 0.126762           0.088051\n",
      "0.930000 0.188428 0.111226           0.077202\n",
      "0.940000 0.161856 0.095570           0.066286\n",
      "0.950000 0.135125 0.079811           0.055314\n",
      "0.960000 0.108260 0.063963           0.044297\n",
      "0.970000 0.081289 0.048042           0.033247\n",
      "0.980000 0.054237 0.032064           0.022173\n",
      "0.990000 0.027132 0.016045           0.011087\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.29\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.028353 0.016475           0.011878\n",
      "0.020000 0.056677 0.032944           0.023733\n",
      "0.030000 0.084946 0.049391           0.035555\n",
      "0.040000 0.113130 0.065799           0.047331\n",
      "0.050000 0.141204 0.082153           0.059051\n",
      "0.060000 0.169137 0.098436           0.070701\n",
      "0.070000 0.196904 0.114632           0.082272\n",
      "0.080000 0.224477 0.130725           0.093752\n",
      "0.090000 0.251828 0.146699           0.105129\n",
      "0.100000 0.278930 0.162537           0.116393\n",
      "0.110000 0.305758 0.178225           0.127532\n",
      "0.120000 0.332283 0.193747           0.138536\n",
      "0.130000 0.358481 0.209087           0.149394\n",
      "0.140000 0.384324 0.224229           0.160095\n",
      "0.150000 0.409789 0.239159           0.170629\n",
      "0.160000 0.434849 0.253863           0.180986\n",
      "0.170000 0.459480 0.268324           0.191156\n",
      "0.180000 0.483657 0.282529           0.201128\n",
      "0.190000 0.507358 0.296464           0.210894\n",
      "0.200000 0.530557 0.310114           0.220443\n",
      "0.210000 0.553233 0.323465           0.229767\n",
      "0.220000 0.575363 0.336506           0.238857\n",
      "0.230000 0.596925 0.349222           0.247703\n",
      "0.240000 0.617898 0.361600           0.256298\n",
      "0.250000 0.638261 0.373629           0.264632\n",
      "0.260000 0.657994 0.385295           0.272699\n",
      "0.270000 0.677078 0.396588           0.280490\n",
      "0.280000 0.695494 0.407496           0.287998\n",
      "0.290000 0.713224 0.418008           0.295215\n",
      "0.300000 0.730249 0.428113           0.302136\n",
      "0.310000 0.746554 0.437802           0.308752\n",
      "0.320000 0.762122 0.447063           0.315059\n",
      "0.330000 0.776938 0.455888           0.321050\n",
      "0.340000 0.790987 0.464269           0.326719\n",
      "0.350000 0.804256 0.472195           0.332061\n",
      "0.360000 0.816731 0.479660           0.337071\n",
      "0.370000 0.828400 0.486655           0.341744\n",
      "0.380000 0.839251 0.493174           0.346077\n",
      "0.390000 0.849274 0.499210           0.350064\n",
      "0.400000 0.858459 0.504756           0.353703\n",
      "0.410000 0.866797 0.509807           0.356990\n",
      "0.420000 0.874279 0.514357           0.359922\n",
      "0.430000 0.880899 0.518402           0.362497\n",
      "0.440000 0.886649 0.521937           0.364712\n",
      "0.450000 0.891524 0.524959           0.366565\n",
      "0.460000 0.895520 0.527465           0.368055\n",
      "0.470000 0.898632 0.529450           0.369181\n",
      "0.480000 0.900856 0.530915           0.369942\n",
      "0.490000 0.902192 0.531855           0.370337\n",
      "0.500000 0.902637 0.532272           0.370366\n",
      "0.510000 0.902192 0.532163           0.370029\n",
      "0.520000 0.900856 0.531528           0.369328\n",
      "0.530000 0.898632 0.530368           0.368263\n",
      "0.540000 0.895520 0.528684           0.366836\n",
      "0.550000 0.891524 0.526477           0.365047\n",
      "0.560000 0.886649 0.523749           0.362900\n",
      "0.570000 0.880899 0.520502           0.360397\n",
      "0.580000 0.874279 0.516740           0.357540\n",
      "0.590000 0.866797 0.512465           0.354332\n",
      "0.600000 0.858459 0.507682           0.350778\n",
      "0.610000 0.849274 0.502394           0.346880\n",
      "0.620000 0.839251 0.496608           0.342643\n",
      "0.630000 0.828400 0.490329           0.338071\n",
      "0.640000 0.816731 0.483561           0.333169\n",
      "0.650000 0.804256 0.476313           0.327943\n",
      "0.660000 0.790987 0.468590           0.322397\n",
      "0.670000 0.776938 0.460400           0.316538\n",
      "0.680000 0.762122 0.451751           0.310371\n",
      "0.690000 0.746554 0.442651           0.303903\n",
      "0.700000 0.730249 0.433109           0.297140\n",
      "0.710000 0.713224 0.423133           0.290090\n",
      "0.720000 0.695494 0.412735           0.282759\n",
      "0.730000 0.677078 0.401923           0.275155\n",
      "0.740000 0.657994 0.390708           0.267287\n",
      "0.750000 0.638261 0.379101           0.259160\n",
      "0.760000 0.617898 0.367113           0.250785\n",
      "0.770000 0.596925 0.354755           0.242169\n",
      "0.780000 0.575363 0.342041           0.233322\n",
      "0.790000 0.553233 0.328981           0.224252\n",
      "0.800000 0.530557 0.315589           0.214968\n",
      "0.810000 0.507358 0.301878           0.205480\n",
      "0.820000 0.483657 0.287861           0.195797\n",
      "0.830000 0.459480 0.273551           0.185929\n",
      "0.840000 0.434849 0.258963           0.175886\n",
      "0.850000 0.409789 0.244111           0.165678\n",
      "0.860000 0.384324 0.229010           0.155315\n",
      "0.870000 0.358481 0.213673           0.144808\n",
      "0.880000 0.332283 0.198116           0.134167\n",
      "0.890000 0.305758 0.182355           0.123402\n",
      "0.900000 0.278930 0.166405           0.112526\n",
      "0.910000 0.251828 0.150280           0.101547\n",
      "0.920000 0.224477 0.133998           0.090479\n",
      "0.930000 0.196904 0.117574           0.079330\n",
      "0.940000 0.169137 0.101024           0.068113\n",
      "0.950000 0.141204 0.084365           0.056839\n",
      "0.960000 0.113130 0.067612           0.045518\n",
      "0.970000 0.084946 0.050783           0.034163\n",
      "0.980000 0.056677 0.033893           0.022784\n",
      "0.990000 0.028353 0.016960           0.011392\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.3\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.029601 0.017412           0.012189\n",
      "0.020000 0.059173 0.034818           0.024355\n",
      "0.030000 0.088686 0.052200           0.036486\n",
      "0.040000 0.118112 0.069542           0.048570\n",
      "0.050000 0.147421 0.086825           0.060596\n",
      "0.060000 0.176585 0.104034           0.072552\n",
      "0.070000 0.205575 0.121150           0.084425\n",
      "0.080000 0.234362 0.138157           0.096205\n",
      "0.090000 0.262917 0.155037           0.107880\n",
      "0.100000 0.291213 0.171775           0.119438\n",
      "0.110000 0.319221 0.188353           0.130868\n",
      "0.120000 0.346915 0.204755           0.142160\n",
      "0.130000 0.374266 0.220965           0.153301\n",
      "0.140000 0.401248 0.236966           0.164282\n",
      "0.150000 0.427834 0.252742           0.175091\n",
      "0.160000 0.453997 0.268279           0.185719\n",
      "0.170000 0.479713 0.283559           0.196154\n",
      "0.180000 0.504955 0.298568           0.206387\n",
      "0.190000 0.529699 0.313292           0.216407\n",
      "0.200000 0.553920 0.327714           0.226206\n",
      "0.210000 0.577594 0.341821           0.235773\n",
      "0.220000 0.600699 0.355599           0.245099\n",
      "0.230000 0.623210 0.369034           0.254176\n",
      "0.240000 0.645107 0.382112           0.262995\n",
      "0.250000 0.666367 0.394820           0.271547\n",
      "0.260000 0.686969 0.407145           0.279824\n",
      "0.270000 0.706893 0.419075           0.287818\n",
      "0.280000 0.726120 0.430599           0.295521\n",
      "0.290000 0.744630 0.441703           0.302927\n",
      "0.300000 0.762405 0.452378           0.310027\n",
      "0.310000 0.779428 0.462612           0.316816\n",
      "0.320000 0.795682 0.472395           0.323287\n",
      "0.330000 0.811150 0.481717           0.329433\n",
      "0.340000 0.825818 0.490568           0.335250\n",
      "0.350000 0.839671 0.498941           0.340730\n",
      "0.360000 0.852695 0.506825           0.345871\n",
      "0.370000 0.864878 0.514212           0.350666\n",
      "0.380000 0.876207 0.521097           0.355110\n",
      "0.390000 0.886672 0.527470           0.359201\n",
      "0.400000 0.896261 0.533327           0.362935\n",
      "0.410000 0.904966 0.538659           0.366307\n",
      "0.420000 0.912778 0.543463           0.369315\n",
      "0.430000 0.919689 0.547733           0.371956\n",
      "0.440000 0.925693 0.551465           0.374228\n",
      "0.450000 0.930782 0.554654           0.376129\n",
      "0.460000 0.934954 0.557297           0.377657\n",
      "0.470000 0.938202 0.559391           0.378811\n",
      "0.480000 0.940525 0.560934           0.379591\n",
      "0.490000 0.941920 0.561924           0.379995\n",
      "0.500000 0.942385 0.562360           0.380025\n",
      "0.510000 0.941920 0.562241           0.379679\n",
      "0.520000 0.940525 0.561566           0.378959\n",
      "0.530000 0.938202 0.560337           0.377865\n",
      "0.540000 0.934954 0.558554           0.376400\n",
      "0.550000 0.930782 0.556218           0.374564\n",
      "0.560000 0.925693 0.553332           0.372360\n",
      "0.570000 0.919689 0.549898           0.369791\n",
      "0.580000 0.912778 0.545919           0.366859\n",
      "0.590000 0.904966 0.541399           0.363567\n",
      "0.600000 0.896261 0.536342           0.359919\n",
      "0.610000 0.886672 0.530753           0.355919\n",
      "0.620000 0.876207 0.524637           0.351571\n",
      "0.630000 0.864878 0.517999           0.346879\n",
      "0.640000 0.852695 0.510846           0.341849\n",
      "0.650000 0.839671 0.503185           0.336486\n",
      "0.660000 0.825818 0.495023           0.330795\n",
      "0.670000 0.811150 0.486368           0.324783\n",
      "0.680000 0.795682 0.477227           0.318455\n",
      "0.690000 0.779428 0.467611           0.311817\n",
      "0.700000 0.762405 0.457527           0.304878\n",
      "0.710000 0.744630 0.446987           0.297644\n",
      "0.720000 0.726120 0.435999           0.290121\n",
      "0.730000 0.706893 0.424574           0.282319\n",
      "0.740000 0.686969 0.412724           0.274245\n",
      "0.750000 0.666367 0.400460           0.265906\n",
      "0.760000 0.645107 0.387794           0.257313\n",
      "0.770000 0.623210 0.374738           0.248472\n",
      "0.780000 0.600699 0.361305           0.239394\n",
      "0.790000 0.577594 0.347507           0.230087\n",
      "0.800000 0.553920 0.333358           0.220561\n",
      "0.810000 0.529699 0.318873           0.210826\n",
      "0.820000 0.504955 0.304064           0.200891\n",
      "0.830000 0.479713 0.288947           0.190766\n",
      "0.840000 0.453997 0.273536           0.180461\n",
      "0.850000 0.427834 0.257847           0.169987\n",
      "0.860000 0.401248 0.241894           0.159354\n",
      "0.870000 0.374266 0.225692           0.148574\n",
      "0.880000 0.346915 0.209259           0.137656\n",
      "0.890000 0.319221 0.192610           0.126611\n",
      "0.900000 0.291213 0.175761           0.115451\n",
      "0.910000 0.262917 0.158729           0.104188\n",
      "0.920000 0.234362 0.141531           0.092831\n",
      "0.930000 0.205575 0.124183           0.081392\n",
      "0.940000 0.176585 0.106702           0.069883\n",
      "0.950000 0.147421 0.089106           0.058316\n",
      "0.960000 0.118112 0.071411           0.046701\n",
      "0.970000 0.088686 0.053636           0.035051\n",
      "0.980000 0.059173 0.035797           0.023376\n",
      "0.990000 0.029601 0.017913           0.011688\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.31\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.030879 0.018389           0.012490\n",
      "0.020000 0.061727 0.036771           0.024956\n",
      "0.030000 0.092514 0.055128           0.037386\n",
      "0.040000 0.123210 0.073441           0.049769\n",
      "0.050000 0.153785 0.091693           0.062091\n",
      "0.060000 0.184208 0.109866           0.074342\n",
      "0.070000 0.214448 0.127940           0.086508\n",
      "0.080000 0.244478 0.145899           0.098578\n",
      "0.090000 0.274266 0.163725           0.110541\n",
      "0.100000 0.303783 0.181399           0.122384\n",
      "0.110000 0.333000 0.198904           0.134096\n",
      "0.120000 0.361889 0.216224           0.145666\n",
      "0.130000 0.390421 0.233339           0.157082\n",
      "0.140000 0.418568 0.250235           0.168333\n",
      "0.150000 0.446301 0.266893           0.179408\n",
      "0.160000 0.473594 0.283296           0.190297\n",
      "0.170000 0.500419 0.299430           0.200989\n",
      "0.180000 0.526751 0.315277           0.211474\n",
      "0.190000 0.552563 0.330822           0.221741\n",
      "0.200000 0.577830 0.346049           0.231781\n",
      "0.210000 0.602526 0.360943           0.241583\n",
      "0.220000 0.626627 0.375488           0.251139\n",
      "0.230000 0.650111 0.389671           0.260439\n",
      "0.240000 0.672952 0.403478           0.269475\n",
      "0.250000 0.695130 0.416893           0.278237\n",
      "0.260000 0.716622 0.429905           0.286717\n",
      "0.270000 0.737406 0.442499           0.294907\n",
      "0.280000 0.757463 0.454663           0.302800\n",
      "0.290000 0.776772 0.466385           0.310387\n",
      "0.300000 0.795314 0.477652           0.317662\n",
      "0.310000 0.813072 0.488455           0.324617\n",
      "0.320000 0.830027 0.498780           0.331246\n",
      "0.330000 0.846163 0.508619           0.337544\n",
      "0.340000 0.861464 0.517962           0.343502\n",
      "0.350000 0.875915 0.526797           0.349118\n",
      "0.360000 0.889501 0.535118           0.354384\n",
      "0.370000 0.902210 0.542914           0.359296\n",
      "0.380000 0.914028 0.550179           0.363849\n",
      "0.390000 0.924944 0.556904           0.368040\n",
      "0.400000 0.934948 0.563083           0.371865\n",
      "0.410000 0.944029 0.568710           0.375319\n",
      "0.420000 0.952178 0.573777           0.378400\n",
      "0.430000 0.959387 0.578281           0.381105\n",
      "0.440000 0.965650 0.582217           0.383433\n",
      "0.450000 0.970959 0.585580           0.385380\n",
      "0.460000 0.975311 0.588366           0.386945\n",
      "0.470000 0.978699 0.590573           0.388127\n",
      "0.480000 0.981122 0.592198           0.388925\n",
      "0.490000 0.982577 0.593239           0.389338\n",
      "0.500000 0.983062 0.593695           0.389368\n",
      "0.510000 0.982577 0.593565           0.389013\n",
      "0.520000 0.981122 0.592848           0.388274\n",
      "0.530000 0.978699 0.591547           0.387153\n",
      "0.540000 0.975311 0.589660           0.385651\n",
      "0.550000 0.970959 0.587190           0.383769\n",
      "0.560000 0.965650 0.584139           0.381510\n",
      "0.570000 0.959387 0.580510           0.378877\n",
      "0.580000 0.952178 0.576306           0.375872\n",
      "0.590000 0.944029 0.571530           0.372499\n",
      "0.600000 0.934948 0.566188           0.368760\n",
      "0.610000 0.924944 0.560283           0.364661\n",
      "0.620000 0.914028 0.553823           0.360206\n",
      "0.630000 0.902210 0.546812           0.355398\n",
      "0.640000 0.889501 0.539257           0.350244\n",
      "0.650000 0.875915 0.531166           0.344748\n",
      "0.660000 0.861464 0.522547           0.338917\n",
      "0.670000 0.846163 0.513407           0.332756\n",
      "0.680000 0.830027 0.503755           0.326272\n",
      "0.690000 0.813072 0.493600           0.319472\n",
      "0.700000 0.795314 0.482953           0.312361\n",
      "0.710000 0.776772 0.471823           0.304949\n",
      "0.720000 0.757463 0.460221           0.297241\n",
      "0.730000 0.737406 0.448159           0.289247\n",
      "0.740000 0.716622 0.435648           0.280974\n",
      "0.750000 0.695130 0.422700           0.272430\n",
      "0.760000 0.672952 0.409327           0.263625\n",
      "0.770000 0.650111 0.395543           0.254568\n",
      "0.780000 0.626627 0.381361           0.245266\n",
      "0.790000 0.602526 0.366795           0.235731\n",
      "0.800000 0.577830 0.351859           0.225971\n",
      "0.810000 0.552563 0.336567           0.215996\n",
      "0.820000 0.526751 0.320934           0.205817\n",
      "0.830000 0.500419 0.304976           0.195443\n",
      "0.840000 0.473594 0.288709           0.184885\n",
      "0.850000 0.446301 0.272147           0.174154\n",
      "0.860000 0.418568 0.255307           0.163261\n",
      "0.870000 0.390421 0.238206           0.152215\n",
      "0.880000 0.361889 0.220860           0.141029\n",
      "0.890000 0.333000 0.203286           0.129714\n",
      "0.900000 0.303783 0.185502           0.118281\n",
      "0.910000 0.274266 0.167525           0.106740\n",
      "0.920000 0.244478 0.149373           0.095105\n",
      "0.930000 0.214448 0.131062           0.083386\n",
      "0.940000 0.184208 0.112612           0.071595\n",
      "0.950000 0.153785 0.094040           0.059744\n",
      "0.960000 0.123210 0.075365           0.047845\n",
      "0.970000 0.092514 0.056605           0.035909\n",
      "0.980000 0.061727 0.037779           0.023948\n",
      "0.990000 0.030879 0.018904           0.011975\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.32\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.032187 0.019407           0.012780\n",
      "0.020000 0.064342 0.038806           0.025536\n",
      "0.030000 0.096434 0.058178           0.038256\n",
      "0.040000 0.128430 0.077504           0.050926\n",
      "0.050000 0.160300 0.096765           0.063535\n",
      "0.060000 0.192012 0.115941           0.076070\n",
      "0.070000 0.223534 0.135014           0.088519\n",
      "0.080000 0.254835 0.153965           0.100870\n",
      "0.090000 0.285885 0.172775           0.113110\n",
      "0.100000 0.316653 0.191425           0.125228\n",
      "0.110000 0.347108 0.209896           0.137212\n",
      "0.120000 0.377221 0.228171           0.149050\n",
      "0.130000 0.406961 0.246230           0.160731\n",
      "0.140000 0.436300 0.264057           0.172243\n",
      "0.150000 0.465209 0.281633           0.183576\n",
      "0.160000 0.493658 0.298941           0.194717\n",
      "0.170000 0.521620 0.315963           0.205657\n",
      "0.180000 0.549067 0.332682           0.216385\n",
      "0.190000 0.575973 0.349083           0.226890\n",
      "0.200000 0.602309 0.365147           0.237162\n",
      "0.210000 0.628052 0.380860           0.247192\n",
      "0.220000 0.653175 0.396206           0.256969\n",
      "0.230000 0.677653 0.411168           0.266485\n",
      "0.240000 0.701462 0.425733           0.275729\n",
      "0.250000 0.724579 0.439886           0.284694\n",
      "0.260000 0.746982 0.453611           0.293370\n",
      "0.270000 0.768646 0.466896           0.301750\n",
      "0.280000 0.789553 0.479728           0.309825\n",
      "0.290000 0.809680 0.492092           0.317588\n",
      "0.300000 0.829008 0.503977           0.325031\n",
      "0.310000 0.847518 0.515371           0.332147\n",
      "0.320000 0.865191 0.526262           0.338929\n",
      "0.330000 0.882011 0.536640           0.345371\n",
      "0.340000 0.897960 0.546492           0.351468\n",
      "0.350000 0.913023 0.555811           0.357212\n",
      "0.360000 0.927185 0.564586           0.362600\n",
      "0.370000 0.940432 0.572807           0.367625\n",
      "0.380000 0.952751 0.580468           0.372284\n",
      "0.390000 0.964130 0.587559           0.376571\n",
      "0.400000 0.974557 0.594074           0.380483\n",
      "0.410000 0.984023 0.600006           0.384017\n",
      "0.420000 0.992517 0.605348           0.387169\n",
      "0.430000 1.000032 0.610096           0.389936\n",
      "0.440000 1.006560 0.614244           0.392316\n",
      "0.450000 1.012094 0.617787           0.394307\n",
      "0.460000 1.016630 0.620722           0.395908\n",
      "0.470000 1.020162 0.623046           0.397116\n",
      "0.480000 1.022688 0.624756           0.397932\n",
      "0.490000 1.024204 0.625850           0.398355\n",
      "0.500000 1.024710 0.626326           0.398384\n",
      "0.510000 1.024204 0.626185           0.398020\n",
      "0.520000 1.022688 0.625425           0.397263\n",
      "0.530000 1.020162 0.624047           0.396115\n",
      "0.540000 1.016630 0.622052           0.394578\n",
      "0.550000 1.012094 0.619442           0.392652\n",
      "0.560000 1.006560 0.616220           0.390340\n",
      "0.570000 1.000032 0.612387           0.387645\n",
      "0.580000 0.992517 0.607947           0.384570\n",
      "0.590000 0.984023 0.602905           0.381117\n",
      "0.600000 0.974557 0.597265           0.377292\n",
      "0.610000 0.964130 0.591033           0.373097\n",
      "0.620000 0.952751 0.584214           0.368538\n",
      "0.630000 0.940432 0.576814           0.363618\n",
      "0.640000 0.927185 0.568841           0.358344\n",
      "0.650000 0.913023 0.560302           0.352721\n",
      "0.660000 0.897960 0.551206           0.346754\n",
      "0.670000 0.882011 0.541561           0.340450\n",
      "0.680000 0.865191 0.531376           0.333816\n",
      "0.690000 0.847518 0.520661           0.326857\n",
      "0.700000 0.829008 0.509426           0.319582\n",
      "0.710000 0.809680 0.497683           0.311997\n",
      "0.720000 0.789553 0.485442           0.304111\n",
      "0.730000 0.768646 0.472715           0.295931\n",
      "0.740000 0.746982 0.459515           0.287466\n",
      "0.750000 0.724579 0.445854           0.278725\n",
      "0.760000 0.701462 0.431746           0.269716\n",
      "0.770000 0.677653 0.417204           0.260449\n",
      "0.780000 0.653175 0.402243           0.250932\n",
      "0.790000 0.628052 0.386876           0.241176\n",
      "0.800000 0.602309 0.371120           0.231190\n",
      "0.810000 0.575973 0.354988           0.220984\n",
      "0.820000 0.549067 0.338498           0.210569\n",
      "0.830000 0.521620 0.321664           0.199956\n",
      "0.840000 0.493658 0.304504           0.189154\n",
      "0.850000 0.465209 0.287034           0.178175\n",
      "0.860000 0.436300 0.269271           0.167029\n",
      "0.870000 0.406961 0.251233           0.155729\n",
      "0.880000 0.377221 0.232937           0.144284\n",
      "0.890000 0.347108 0.214401           0.132707\n",
      "0.900000 0.316653 0.195643           0.121010\n",
      "0.910000 0.285885 0.176682           0.109203\n",
      "0.920000 0.254835 0.157536           0.097299\n",
      "0.930000 0.223534 0.138224           0.085310\n",
      "0.940000 0.192012 0.118765           0.073247\n",
      "0.950000 0.160300 0.099178           0.061122\n",
      "0.960000 0.128430 0.079482           0.048948\n",
      "0.970000 0.096434 0.059697           0.036737\n",
      "0.980000 0.064342 0.039842           0.024500\n",
      "0.990000 0.032187 0.019936           0.012251\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.33\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.033527 0.020467           0.013060\n",
      "0.020000 0.067021 0.040926           0.026095\n",
      "0.030000 0.100448 0.061355           0.039093\n",
      "0.040000 0.133777 0.081736           0.052041\n",
      "0.050000 0.166973 0.102048           0.064925\n",
      "0.060000 0.200005 0.122271           0.077734\n",
      "0.070000 0.232839 0.142384           0.090456\n",
      "0.080000 0.265444 0.162368           0.103076\n",
      "0.090000 0.297787 0.182202           0.115584\n",
      "0.100000 0.329835 0.201868           0.127967\n",
      "0.110000 0.361558 0.221346           0.140213\n",
      "0.120000 0.392925 0.240615           0.152309\n",
      "0.130000 0.423904 0.259658           0.164245\n",
      "0.140000 0.454464 0.278455           0.176009\n",
      "0.150000 0.484576 0.296987           0.187589\n",
      "0.160000 0.514209 0.315236           0.198973\n",
      "0.170000 0.543335 0.333183           0.210152\n",
      "0.180000 0.571925 0.350812           0.221113\n",
      "0.190000 0.599951 0.368103           0.231848\n",
      "0.200000 0.627384 0.385040           0.242344\n",
      "0.210000 0.654198 0.401606           0.252592\n",
      "0.220000 0.680367 0.417785           0.262582\n",
      "0.230000 0.705864 0.433559           0.272305\n",
      "0.240000 0.730665 0.448914           0.281751\n",
      "0.250000 0.754744 0.463833           0.290911\n",
      "0.260000 0.778079 0.478303           0.299776\n",
      "0.270000 0.800646 0.492307           0.308338\n",
      "0.280000 0.822422 0.505833           0.316589\n",
      "0.290000 0.843387 0.518867           0.324520\n",
      "0.300000 0.863520 0.531395           0.332125\n",
      "0.310000 0.882800 0.543405           0.339396\n",
      "0.320000 0.901210 0.554884           0.346326\n",
      "0.330000 0.918730 0.565822           0.352908\n",
      "0.340000 0.935343 0.576206           0.359137\n",
      "0.350000 0.951033 0.586027           0.365006\n",
      "0.360000 0.965785 0.595275           0.370510\n",
      "0.370000 0.979583 0.603939           0.375644\n",
      "0.380000 0.992415 0.612012           0.380403\n",
      "0.390000 1.004267 0.619484           0.384783\n",
      "0.400000 1.015129 0.626349           0.388780\n",
      "0.410000 1.024988 0.632598           0.392390\n",
      "0.420000 1.033836 0.638226           0.395610\n",
      "0.430000 1.041664 0.643227           0.398437\n",
      "0.440000 1.048463 0.647595           0.400868\n",
      "0.450000 1.054228 0.651327           0.402902\n",
      "0.460000 1.058953 0.654417           0.404536\n",
      "0.470000 1.062632 0.656862           0.405770\n",
      "0.480000 1.065263 0.658660           0.406603\n",
      "0.490000 1.066843 0.659809           0.407034\n",
      "0.500000 1.067369 0.660306           0.407063\n",
      "0.510000 1.066843 0.660153           0.406690\n",
      "0.520000 1.065263 0.659347           0.405916\n",
      "0.530000 1.062632 0.657890           0.404743\n",
      "0.540000 1.058953 0.655782           0.403171\n",
      "0.550000 1.054228 0.653026           0.401202\n",
      "0.560000 1.048463 0.649624           0.398839\n",
      "0.570000 1.041664 0.645579           0.396085\n",
      "0.580000 1.033836 0.640894           0.392942\n",
      "0.590000 1.024988 0.635575           0.389413\n",
      "0.600000 1.015129 0.629625           0.385504\n",
      "0.610000 1.004267 0.623050           0.381217\n",
      "0.620000 0.992415 0.615857           0.376558\n",
      "0.630000 0.979583 0.608053           0.371531\n",
      "0.640000 0.965785 0.599644           0.366141\n",
      "0.650000 0.951033 0.590639           0.360395\n",
      "0.660000 0.935343 0.581046           0.354297\n",
      "0.670000 0.918730 0.570874           0.347856\n",
      "0.680000 0.901210 0.560134           0.341076\n",
      "0.690000 0.882800 0.548835           0.333965\n",
      "0.700000 0.863520 0.536989           0.326531\n",
      "0.710000 0.843387 0.524606           0.318781\n",
      "0.720000 0.822422 0.511700           0.310723\n",
      "0.730000 0.800646 0.498281           0.302364\n",
      "0.740000 0.778079 0.484364           0.293715\n",
      "0.750000 0.754744 0.469961           0.284783\n",
      "0.760000 0.730665 0.455087           0.275578\n",
      "0.770000 0.705864 0.439756           0.266108\n",
      "0.780000 0.680367 0.423983           0.256384\n",
      "0.790000 0.654198 0.407783           0.246415\n",
      "0.800000 0.627384 0.391172           0.236212\n",
      "0.810000 0.599951 0.374166           0.225784\n",
      "0.820000 0.571925 0.356782           0.215143\n",
      "0.830000 0.543335 0.339037           0.204298\n",
      "0.840000 0.514209 0.320948           0.193262\n",
      "0.850000 0.484576 0.302532           0.182044\n",
      "0.860000 0.454464 0.283808           0.170656\n",
      "0.870000 0.423904 0.264794           0.159109\n",
      "0.880000 0.392925 0.245509           0.147416\n",
      "0.890000 0.361558 0.225970           0.135588\n",
      "0.900000 0.329835 0.206199           0.123636\n",
      "0.910000 0.297787 0.186213           0.111573\n",
      "0.920000 0.265444 0.166033           0.099411\n",
      "0.930000 0.232839 0.145679           0.087161\n",
      "0.940000 0.200005 0.125169           0.074836\n",
      "0.950000 0.166973 0.104525           0.062448\n",
      "0.960000 0.133777 0.083767           0.050010\n",
      "0.970000 0.100448 0.062914           0.037534\n",
      "0.980000 0.067021 0.041989           0.025032\n",
      "0.990000 0.033527 0.021011           0.012516\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.34\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.034900 0.021571           0.013329\n",
      "0.020000 0.069765 0.043133           0.026632\n",
      "0.030000 0.104562 0.064665           0.039897\n",
      "0.040000 0.139256 0.086145           0.053111\n",
      "0.050000 0.173812 0.107551           0.066260\n",
      "0.060000 0.208196 0.128863           0.079333\n",
      "0.070000 0.242375 0.150060           0.092315\n",
      "0.080000 0.276315 0.171120           0.105195\n",
      "0.090000 0.309982 0.192022           0.117960\n",
      "0.100000 0.343343 0.212746           0.130597\n",
      "0.110000 0.376366 0.233271           0.143094\n",
      "0.120000 0.409017 0.253577           0.155439\n",
      "0.130000 0.441264 0.273644           0.167620\n",
      "0.140000 0.473076 0.293451           0.179625\n",
      "0.150000 0.504421 0.312979           0.191442\n",
      "0.160000 0.535268 0.332208           0.203060\n",
      "0.170000 0.565587 0.351119           0.214468\n",
      "0.180000 0.595348 0.369693           0.225654\n",
      "0.190000 0.624521 0.387913           0.236608\n",
      "0.200000 0.653078 0.405758           0.247319\n",
      "0.210000 0.680990 0.423213           0.257777\n",
      "0.220000 0.708230 0.440258           0.267972\n",
      "0.230000 0.734772 0.456878           0.277894\n",
      "0.240000 0.760588 0.473055           0.287533\n",
      "0.250000 0.785654 0.488773           0.296881\n",
      "0.260000 0.809944 0.504017           0.305927\n",
      "0.270000 0.833435 0.518771           0.314664\n",
      "0.280000 0.856104 0.533020           0.323083\n",
      "0.290000 0.877927 0.546750           0.331177\n",
      "0.300000 0.898884 0.559948           0.338937\n",
      "0.310000 0.918954 0.572599           0.346356\n",
      "0.320000 0.938118 0.584691           0.353427\n",
      "0.330000 0.956355 0.596212           0.360144\n",
      "0.340000 0.973649 0.607150           0.366499\n",
      "0.350000 0.989981 0.617494           0.372488\n",
      "0.360000 1.005337 0.627233           0.378104\n",
      "0.370000 1.019701 0.636358           0.383343\n",
      "0.380000 1.033058 0.644859           0.388199\n",
      "0.390000 1.045396 0.652728           0.392668\n",
      "0.400000 1.056702 0.659956           0.396746\n",
      "0.410000 1.066965 0.666537           0.400429\n",
      "0.420000 1.076175 0.672462           0.403714\n",
      "0.430000 1.084324 0.677726           0.406597\n",
      "0.440000 1.091402 0.682324           0.409078\n",
      "0.450000 1.097403 0.686251           0.411152\n",
      "0.460000 1.102321 0.689501           0.412820\n",
      "0.470000 1.106151 0.692073           0.414078\n",
      "0.480000 1.108890 0.693963           0.414927\n",
      "0.490000 1.110534 0.695168           0.415366\n",
      "0.500000 1.111082 0.695688           0.415395\n",
      "0.510000 1.110534 0.695521           0.415013\n",
      "0.520000 1.108890 0.694667           0.414223\n",
      "0.530000 1.106151 0.693127           0.413024\n",
      "0.540000 1.102321 0.690902           0.411419\n",
      "0.550000 1.097403 0.687993           0.409410\n",
      "0.560000 1.091402 0.684404           0.406997\n",
      "0.570000 1.084324 0.680138           0.404186\n",
      "0.580000 1.076175 0.675198           0.400978\n",
      "0.590000 1.066965 0.669589           0.397376\n",
      "0.600000 1.056702 0.663316           0.393386\n",
      "0.610000 1.045396 0.656385           0.389011\n",
      "0.620000 1.033058 0.648803           0.384256\n",
      "0.630000 1.019701 0.640576           0.379125\n",
      "0.640000 1.005337 0.631713           0.373624\n",
      "0.650000 0.989981 0.622222           0.367760\n",
      "0.660000 0.973649 0.612112           0.361537\n",
      "0.670000 0.956355 0.601392           0.354963\n",
      "0.680000 0.938118 0.590074           0.348044\n",
      "0.690000 0.918954 0.578167           0.340788\n",
      "0.700000 0.898884 0.565684           0.333201\n",
      "0.710000 0.877927 0.552636           0.325292\n",
      "0.720000 0.856104 0.539035           0.317068\n",
      "0.730000 0.833435 0.524896           0.308539\n",
      "0.740000 0.809944 0.510232           0.299712\n",
      "0.750000 0.785654 0.495057           0.290597\n",
      "0.760000 0.760588 0.479385           0.281203\n",
      "0.770000 0.734772 0.463232           0.271540\n",
      "0.780000 0.708230 0.446614           0.261617\n",
      "0.790000 0.680990 0.429546           0.251444\n",
      "0.800000 0.653078 0.412046           0.241032\n",
      "0.810000 0.624521 0.394130           0.230391\n",
      "0.820000 0.595348 0.375815           0.219532\n",
      "0.830000 0.565587 0.357121           0.208466\n",
      "0.840000 0.535268 0.338064           0.197203\n",
      "0.850000 0.504421 0.318664           0.185756\n",
      "0.860000 0.473076 0.298940           0.174136\n",
      "0.870000 0.441264 0.278910           0.162354\n",
      "0.880000 0.409017 0.258595           0.150422\n",
      "0.890000 0.376366 0.238013           0.138352\n",
      "0.900000 0.343343 0.217187           0.126157\n",
      "0.910000 0.309982 0.196135           0.113847\n",
      "0.920000 0.276315 0.174878           0.101437\n",
      "0.930000 0.242375 0.153438           0.088937\n",
      "0.940000 0.208196 0.131835           0.076361\n",
      "0.950000 0.173812 0.110091           0.063721\n",
      "0.960000 0.139256 0.088227           0.051029\n",
      "0.970000 0.104562 0.066264           0.038298\n",
      "0.980000 0.069765 0.044224           0.025542\n",
      "0.990000 0.034900 0.022129           0.012771\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.35000000000000003\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.036307 0.022722           0.013586\n",
      "0.020000 0.072579 0.045433           0.027146\n",
      "0.030000 0.108779 0.068112           0.040667\n",
      "0.040000 0.144872 0.090736           0.054136\n",
      "0.050000 0.180821 0.113282           0.067539\n",
      "0.060000 0.216593 0.135729           0.080863\n",
      "0.070000 0.252150 0.158054           0.094096\n",
      "0.080000 0.287459 0.180234           0.107224\n",
      "0.090000 0.322483 0.202249           0.120235\n",
      "0.100000 0.357190 0.224075           0.133115\n",
      "0.110000 0.391544 0.245691           0.145853\n",
      "0.120000 0.425512 0.267076           0.158436\n",
      "0.130000 0.459060 0.288209           0.170851\n",
      "0.140000 0.492155 0.309068           0.183087\n",
      "0.150000 0.524764 0.329632           0.195131\n",
      "0.160000 0.556855 0.349882           0.206973\n",
      "0.170000 0.588397 0.369797           0.218600\n",
      "0.180000 0.619358 0.389357           0.230001\n",
      "0.190000 0.649707 0.408542           0.241166\n",
      "0.200000 0.679416 0.427333           0.252083\n",
      "0.210000 0.708454 0.445712           0.262742\n",
      "0.220000 0.736793 0.463661           0.273132\n",
      "0.230000 0.764405 0.481160           0.283244\n",
      "0.240000 0.791262 0.498194           0.293069\n",
      "0.250000 0.817339 0.514744           0.302595\n",
      "0.260000 0.842609 0.530794           0.311815\n",
      "0.270000 0.867047 0.546327           0.320720\n",
      "0.280000 0.890630 0.561329           0.329300\n",
      "0.290000 0.913334 0.575785           0.337549\n",
      "0.300000 0.935136 0.589679           0.345457\n",
      "0.310000 0.956016 0.602997           0.353018\n",
      "0.320000 0.975952 0.615727           0.360225\n",
      "0.330000 0.994925 0.627855           0.367070\n",
      "0.340000 1.012916 0.639369           0.373547\n",
      "0.350000 1.029907 0.650257           0.379650\n",
      "0.360000 1.045882 0.660509           0.385373\n",
      "0.370000 1.060825 0.670113           0.390712\n",
      "0.380000 1.074721 0.679061           0.395660\n",
      "0.390000 1.087556 0.687342           0.400214\n",
      "0.400000 1.099318 0.694949           0.404370\n",
      "0.410000 1.109995 0.701873           0.408123\n",
      "0.420000 1.119577 0.708107           0.411470\n",
      "0.430000 1.128054 0.713646           0.414408\n",
      "0.440000 1.135418 0.718482           0.416935\n",
      "0.450000 1.141661 0.722612           0.419049\n",
      "0.460000 1.146777 0.726030           0.420747\n",
      "0.470000 1.150762 0.728732           0.422029\n",
      "0.480000 1.153611 0.730717           0.422894\n",
      "0.490000 1.155321 0.731981           0.423340\n",
      "0.500000 1.155892 0.732523           0.423368\n",
      "0.510000 1.155321 0.732342           0.422979\n",
      "0.520000 1.153611 0.731438           0.422172\n",
      "0.530000 1.150762 0.729812           0.420950\n",
      "0.540000 1.146777 0.727464           0.419313\n",
      "0.550000 1.141661 0.724397           0.417264\n",
      "0.560000 1.135418 0.720613           0.414805\n",
      "0.570000 1.128054 0.716115           0.411939\n",
      "0.580000 1.119577 0.710909           0.408668\n",
      "0.590000 1.109995 0.704999           0.404997\n",
      "0.600000 1.099318 0.698389           0.400929\n",
      "0.610000 1.087556 0.691087           0.396469\n",
      "0.620000 1.074721 0.683099           0.391622\n",
      "0.630000 1.060825 0.674433           0.386392\n",
      "0.640000 1.045882 0.665097           0.380785\n",
      "0.650000 1.029907 0.655099           0.374808\n",
      "0.660000 1.012916 0.644451           0.368465\n",
      "0.670000 0.994925 0.633160           0.361764\n",
      "0.680000 0.975952 0.621240           0.354712\n",
      "0.690000 0.956016 0.608700           0.347316\n",
      "0.700000 0.935136 0.595553           0.339583\n",
      "0.710000 0.913334 0.581812           0.331522\n",
      "0.720000 0.890630 0.567490           0.323140\n",
      "0.730000 0.867047 0.552601           0.314447\n",
      "0.740000 0.842609 0.537159           0.305450\n",
      "0.750000 0.817339 0.521179           0.296160\n",
      "0.760000 0.791262 0.504676           0.286586\n",
      "0.770000 0.764405 0.487668           0.276737\n",
      "0.780000 0.736793 0.470170           0.266623\n",
      "0.790000 0.708454 0.452199           0.256256\n",
      "0.800000 0.679416 0.433772           0.245644\n",
      "0.810000 0.649707 0.414909           0.234799\n",
      "0.820000 0.619358 0.395626           0.223731\n",
      "0.830000 0.588397 0.375944           0.212453\n",
      "0.840000 0.556855 0.355880           0.200975\n",
      "0.850000 0.524764 0.335455           0.189308\n",
      "0.860000 0.492155 0.314689           0.177465\n",
      "0.870000 0.459060 0.293602           0.165458\n",
      "0.880000 0.425512 0.272215           0.153297\n",
      "0.890000 0.391544 0.250548           0.140997\n",
      "0.900000 0.357190 0.228623           0.128568\n",
      "0.910000 0.322483 0.206461           0.116023\n",
      "0.920000 0.287459 0.184084           0.103375\n",
      "0.930000 0.252150 0.161514           0.090636\n",
      "0.940000 0.216593 0.138773           0.077820\n",
      "0.950000 0.180821 0.115884           0.064938\n",
      "0.960000 0.144872 0.092868           0.052004\n",
      "0.970000 0.108779 0.069749           0.039030\n",
      "0.980000 0.072579 0.046550           0.026029\n",
      "0.990000 0.036307 0.023292           0.013015\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.36\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.037751 0.023919           0.013831\n",
      "0.020000 0.075464 0.047828           0.027637\n",
      "0.030000 0.113103 0.071702           0.041402\n",
      "0.040000 0.150631 0.095517           0.055114\n",
      "0.050000 0.188010 0.119251           0.068759\n",
      "0.060000 0.225203 0.142879           0.082324\n",
      "0.070000 0.262174 0.166378           0.095795\n",
      "0.080000 0.298886 0.189726           0.109160\n",
      "0.090000 0.335303 0.212898           0.122406\n",
      "0.100000 0.371390 0.235871           0.135518\n",
      "0.110000 0.407109 0.258624           0.148486\n",
      "0.120000 0.442428 0.281132           0.161295\n",
      "0.130000 0.477309 0.303375           0.173934\n",
      "0.140000 0.511719 0.325329           0.186390\n",
      "0.150000 0.545625 0.346973           0.198652\n",
      "0.160000 0.578992 0.368285           0.210706\n",
      "0.170000 0.611787 0.389245           0.222543\n",
      "0.180000 0.643979 0.409830           0.234149\n",
      "0.190000 0.675535 0.430021           0.245514\n",
      "0.200000 0.706425 0.449797           0.256628\n",
      "0.210000 0.736617 0.469139           0.267478\n",
      "0.220000 0.766083 0.488027           0.278056\n",
      "0.230000 0.794792 0.506443           0.288349\n",
      "0.240000 0.822718 0.524368           0.298350\n",
      "0.250000 0.849831 0.541783           0.308048\n",
      "0.260000 0.876105 0.558672           0.317433\n",
      "0.270000 0.901515 0.575018           0.326497\n",
      "0.280000 0.926035 0.590803           0.335232\n",
      "0.290000 0.949642 0.606013           0.343628\n",
      "0.300000 0.972311 0.620632           0.351678\n",
      "0.310000 0.994020 0.634645           0.359375\n",
      "0.320000 1.014749 0.648039           0.366710\n",
      "0.330000 1.034476 0.660798           0.373678\n",
      "0.340000 1.053182 0.672912           0.380270\n",
      "0.350000 1.070849 0.684367           0.386483\n",
      "0.360000 1.087459 0.695151           0.392308\n",
      "0.370000 1.102996 0.705254           0.397742\n",
      "0.380000 1.117444 0.714666           0.402779\n",
      "0.390000 1.130790 0.723376           0.407414\n",
      "0.400000 1.143020 0.731377           0.411643\n",
      "0.410000 1.154121 0.738659           0.415463\n",
      "0.420000 1.164084 0.745215           0.418869\n",
      "0.430000 1.172898 0.751038           0.421859\n",
      "0.440000 1.180554 0.756123           0.424431\n",
      "0.450000 1.187045 0.760464           0.426582\n",
      "0.460000 1.192365 0.764055           0.428310\n",
      "0.470000 1.196508 0.766894           0.429614\n",
      "0.480000 1.199471 0.768978           0.430493\n",
      "0.490000 1.201249 0.770303           0.430946\n",
      "0.500000 1.201842 0.770868           0.430974\n",
      "0.510000 1.201249 0.770672           0.430577\n",
      "0.520000 1.199471 0.769715           0.429755\n",
      "0.530000 1.196508 0.767998           0.428510\n",
      "0.540000 1.192365 0.765522           0.426843\n",
      "0.550000 1.187045 0.762289           0.424756\n",
      "0.560000 1.180554 0.758302           0.422252\n",
      "0.570000 1.172898 0.753565           0.419333\n",
      "0.580000 1.164084 0.748081           0.416003\n",
      "0.590000 1.154121 0.741856           0.412265\n",
      "0.600000 1.143020 0.734896           0.408124\n",
      "0.610000 1.130790 0.727207           0.403583\n",
      "0.620000 1.117444 0.718797           0.398648\n",
      "0.630000 1.102996 0.709673           0.393323\n",
      "0.640000 1.087459 0.699844           0.387615\n",
      "0.650000 1.070849 0.689320           0.381529\n",
      "0.660000 1.053182 0.678110           0.375072\n",
      "0.670000 1.034476 0.666226           0.368250\n",
      "0.680000 1.014749 0.653678           0.361071\n",
      "0.690000 0.994020 0.640479           0.353541\n",
      "0.700000 0.972311 0.626641           0.345669\n",
      "0.710000 0.949642 0.612179           0.337463\n",
      "0.720000 0.926035 0.597105           0.328930\n",
      "0.730000 0.901515 0.581435           0.320080\n",
      "0.740000 0.876105 0.565183           0.310922\n",
      "0.750000 0.849831 0.548366           0.301465\n",
      "0.760000 0.822718 0.530999           0.291719\n",
      "0.770000 0.794792 0.513100           0.281693\n",
      "0.780000 0.766083 0.494685           0.271398\n",
      "0.790000 0.736617 0.475774           0.260844\n",
      "0.800000 0.706425 0.456384           0.250041\n",
      "0.810000 0.675535 0.436534           0.239002\n",
      "0.820000 0.643979 0.416243           0.227736\n",
      "0.830000 0.611787 0.395532           0.216255\n",
      "0.840000 0.578992 0.374421           0.204571\n",
      "0.850000 0.545625 0.352930           0.192695\n",
      "0.860000 0.511719 0.331079           0.180640\n",
      "0.870000 0.477309 0.308892           0.168417\n",
      "0.880000 0.442428 0.286388           0.156039\n",
      "0.890000 0.407109 0.263592           0.143518\n",
      "0.900000 0.371390 0.240523           0.130866\n",
      "0.910000 0.335303 0.217206           0.118097\n",
      "0.920000 0.298886 0.193663           0.105223\n",
      "0.930000 0.262174 0.169918           0.092256\n",
      "0.940000 0.225203 0.145992           0.079210\n",
      "0.950000 0.188010 0.121911           0.066098\n",
      "0.960000 0.150631 0.097698           0.052933\n",
      "0.970000 0.113103 0.073376           0.039727\n",
      "0.980000 0.075464 0.048970           0.026494\n",
      "0.990000 0.037751 0.024503           0.013248\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.37\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.039231 0.025166           0.014065\n",
      "0.020000 0.078424 0.050321           0.028103\n",
      "0.030000 0.117539 0.075439           0.042100\n",
      "0.040000 0.156539 0.100495           0.056044\n",
      "0.050000 0.195383 0.125464           0.069919\n",
      "0.060000 0.234035 0.150323           0.083712\n",
      "0.070000 0.272456 0.175045           0.097411\n",
      "0.080000 0.310608 0.199607           0.111001\n",
      "0.090000 0.348454 0.223984           0.124470\n",
      "0.100000 0.385956 0.248153           0.137803\n",
      "0.110000 0.423076 0.272088           0.150989\n",
      "0.120000 0.459780 0.295766           0.164014\n",
      "0.130000 0.496029 0.319164           0.176865\n",
      "0.140000 0.531789 0.342258           0.189531\n",
      "0.150000 0.567024 0.365026           0.201999\n",
      "0.160000 0.601700 0.387444           0.214256\n",
      "0.170000 0.635782 0.409491           0.226291\n",
      "0.180000 0.669236 0.431144           0.238092\n",
      "0.190000 0.702030 0.452382           0.249649\n",
      "0.200000 0.734131 0.473183           0.260949\n",
      "0.210000 0.765508 0.493527           0.271981\n",
      "0.220000 0.796129 0.513393           0.282736\n",
      "0.230000 0.825964 0.532762           0.293202\n",
      "0.240000 0.854985 0.551614           0.303371\n",
      "0.250000 0.883161 0.569931           0.313231\n",
      "0.260000 0.910466 0.587693           0.322773\n",
      "0.270000 0.936873 0.604883           0.331989\n",
      "0.280000 0.962355 0.621485           0.340870\n",
      "0.290000 0.986887 0.637480           0.349407\n",
      "0.300000 1.010445 0.652853           0.357592\n",
      "0.310000 1.033006 0.667589           0.365417\n",
      "0.320000 1.054548 0.681673           0.372875\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.330000 1.075048 0.695090           0.379958\n",
      "0.340000 1.094488 0.707827           0.386661\n",
      "0.350000 1.112848 0.719871           0.392977\n",
      "0.360000 1.130110 0.731210           0.398900\n",
      "0.370000 1.146256 0.741832           0.404424\n",
      "0.380000 1.161271 0.751727           0.409544\n",
      "0.390000 1.175140 0.760884           0.414256\n",
      "0.400000 1.187849 0.769294           0.418556\n",
      "0.410000 1.199386 0.776948           0.422438\n",
      "0.420000 1.209740 0.783839           0.425901\n",
      "0.430000 1.218899 0.789958           0.428941\n",
      "0.440000 1.226856 0.795301           0.431555\n",
      "0.450000 1.233602 0.799861           0.433741\n",
      "0.460000 1.239130 0.803633           0.435497\n",
      "0.470000 1.243436 0.806614           0.436822\n",
      "0.480000 1.246514 0.808800           0.437715\n",
      "0.490000 1.248362 0.810188           0.438175\n",
      "0.500000 1.248979 0.810776           0.438202\n",
      "0.510000 1.248362 0.810565           0.437797\n",
      "0.520000 1.246514 0.809553           0.436961\n",
      "0.530000 1.243436 0.807742           0.435694\n",
      "0.540000 1.239130 0.805132           0.433998\n",
      "0.550000 1.233602 0.801727           0.431875\n",
      "0.560000 1.226856 0.797528           0.429328\n",
      "0.570000 1.218899 0.792540           0.426359\n",
      "0.580000 1.209740 0.786767           0.422973\n",
      "0.590000 1.199386 0.780215           0.419171\n",
      "0.600000 1.187849 0.772890           0.414960\n",
      "0.610000 1.175140 0.764798           0.410342\n",
      "0.620000 1.161271 0.755948           0.405323\n",
      "0.630000 1.146256 0.746347           0.399909\n",
      "0.640000 1.130110 0.736005           0.394104\n",
      "0.650000 1.112848 0.724932           0.387916\n",
      "0.660000 1.094488 0.713139           0.381350\n",
      "0.670000 1.075048 0.700635           0.374413\n",
      "0.680000 1.054548 0.687435           0.367113\n",
      "0.690000 1.033006 0.673550           0.359456\n",
      "0.700000 1.010445 0.658993           0.351452\n",
      "0.710000 0.986887 0.643780           0.343107\n",
      "0.720000 0.962355 0.627923           0.334431\n",
      "0.730000 0.936873 0.611440           0.325433\n",
      "0.740000 0.910466 0.594345           0.316121\n",
      "0.750000 0.883161 0.576656           0.306505\n",
      "0.760000 0.854985 0.558390           0.296595\n",
      "0.770000 0.825964 0.539564           0.286401\n",
      "0.780000 0.796129 0.520196           0.275933\n",
      "0.790000 0.765508 0.500306           0.265202\n",
      "0.800000 0.734131 0.479913           0.254219\n",
      "0.810000 0.702030 0.459036           0.242994\n",
      "0.820000 0.669236 0.437697           0.231540\n",
      "0.830000 0.635782 0.415915           0.219867\n",
      "0.840000 0.601700 0.393713           0.207987\n",
      "0.850000 0.567024 0.371112           0.195913\n",
      "0.860000 0.531789 0.348134           0.183656\n",
      "0.870000 0.496029 0.324801           0.171228\n",
      "0.880000 0.459780 0.301136           0.158643\n",
      "0.890000 0.423076 0.277163           0.145913\n",
      "0.900000 0.385956 0.252906           0.133050\n",
      "0.910000 0.348454 0.228387           0.120067\n",
      "0.920000 0.310608 0.203630           0.106978\n",
      "0.930000 0.272456 0.178661           0.093795\n",
      "0.940000 0.234035 0.153504           0.080531\n",
      "0.950000 0.195383 0.128183           0.067200\n",
      "0.960000 0.156539 0.102723           0.053815\n",
      "0.970000 0.117539 0.077150           0.040389\n",
      "0.980000 0.078424 0.051488           0.026936\n",
      "0.990000 0.039231 0.025763           0.013468\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.38\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.040751 0.026465           0.014286\n",
      "0.020000 0.081461 0.052917           0.028545\n",
      "0.030000 0.122091 0.079329           0.042762\n",
      "0.040000 0.162601 0.105677           0.056924\n",
      "0.050000 0.202950 0.131933           0.071017\n",
      "0.060000 0.243099 0.158071           0.085027\n",
      "0.070000 0.283008 0.184067           0.098941\n",
      "0.080000 0.322637 0.209893           0.112744\n",
      "0.090000 0.361949 0.235525           0.126424\n",
      "0.100000 0.400903 0.260936           0.139966\n",
      "0.110000 0.439461 0.286102           0.153359\n",
      "0.120000 0.477586 0.310998           0.166588\n",
      "0.130000 0.515239 0.335599           0.179641\n",
      "0.140000 0.552384 0.359879           0.192505\n",
      "0.150000 0.588984 0.383816           0.205167\n",
      "0.160000 0.625002 0.407386           0.217616\n",
      "0.170000 0.660404 0.430564           0.229840\n",
      "0.180000 0.695154 0.453328           0.241826\n",
      "0.190000 0.729218 0.475655           0.253563\n",
      "0.200000 0.762562 0.497523           0.265039\n",
      "0.210000 0.795154 0.518910           0.276244\n",
      "0.220000 0.826961 0.539794           0.287167\n",
      "0.230000 0.857952 0.560155           0.297796\n",
      "0.240000 0.888096 0.579973           0.308123\n",
      "0.250000 0.917364 0.599227           0.318137\n",
      "0.260000 0.945726 0.617897           0.327829\n",
      "0.270000 0.973155 0.635967           0.337188\n",
      "0.280000 0.999624 0.653417           0.346207\n",
      "0.290000 1.025106 0.670229           0.354877\n",
      "0.300000 1.049577 0.686388           0.363189\n",
      "0.310000 1.073011 0.701876           0.371136\n",
      "0.320000 1.095387 0.716678           0.378710\n",
      "0.330000 1.116682 0.730779           0.385903\n",
      "0.340000 1.136875 0.744165           0.392710\n",
      "0.350000 1.155946 0.756822           0.399124\n",
      "0.360000 1.173876 0.768737           0.405138\n",
      "0.370000 1.190647 0.779899           0.410748\n",
      "0.380000 1.206244 0.790296           0.415948\n",
      "0.390000 1.220650 0.799918           0.420732\n",
      "0.400000 1.233851 0.808753           0.425098\n",
      "0.410000 1.245835 0.816795           0.429041\n",
      "0.420000 1.256590 0.824033           0.432557\n",
      "0.430000 1.266104 0.830461           0.435643\n",
      "0.440000 1.274369 0.836072           0.438297\n",
      "0.450000 1.281376 0.840860           0.440516\n",
      "0.460000 1.287118 0.844820           0.442299\n",
      "0.470000 1.291591 0.847947           0.443643\n",
      "0.480000 1.294788 0.850239           0.444549\n",
      "0.490000 1.296708 0.851693           0.445016\n",
      "0.500000 1.297348 0.852306           0.445042\n",
      "0.510000 1.296708 0.852078           0.444630\n",
      "0.520000 1.294788 0.851008           0.443780\n",
      "0.530000 1.291591 0.849099           0.442492\n",
      "0.540000 1.287118 0.846350           0.440769\n",
      "0.550000 1.281376 0.842764           0.438612\n",
      "0.560000 1.274369 0.838344           0.436024\n",
      "0.570000 1.266104 0.833095           0.433008\n",
      "0.580000 1.256590 0.827022           0.429568\n",
      "0.590000 1.245835 0.820129           0.425706\n",
      "0.600000 1.233851 0.812423           0.421428\n",
      "0.610000 1.220650 0.803912           0.416738\n",
      "0.620000 1.206244 0.794604           0.411640\n",
      "0.630000 1.190647 0.784507           0.406140\n",
      "0.640000 1.173876 0.773631           0.400244\n",
      "0.650000 1.155946 0.761987           0.393959\n",
      "0.660000 1.136875 0.749585           0.387289\n",
      "0.670000 1.116682 0.736438           0.380244\n",
      "0.680000 1.095387 0.722558           0.372829\n",
      "0.690000 1.073011 0.707959           0.365053\n",
      "0.700000 1.049577 0.692654           0.356923\n",
      "0.710000 1.025106 0.676659           0.348448\n",
      "0.720000 0.999624 0.659988           0.339636\n",
      "0.730000 0.973155 0.642659           0.330497\n",
      "0.740000 0.945726 0.624687           0.321039\n",
      "0.750000 0.917364 0.606091           0.311273\n",
      "0.760000 0.888096 0.586888           0.301208\n",
      "0.770000 0.857952 0.567097           0.290855\n",
      "0.780000 0.826961 0.546737           0.280224\n",
      "0.790000 0.795154 0.525829           0.269325\n",
      "0.800000 0.762562 0.504392           0.258171\n",
      "0.810000 0.729218 0.482447           0.246771\n",
      "0.820000 0.695154 0.460016           0.235138\n",
      "0.830000 0.660404 0.437121           0.223283\n",
      "0.840000 0.625002 0.413784           0.211218\n",
      "0.850000 0.588984 0.390028           0.198956\n",
      "0.860000 0.552384 0.365876           0.186508\n",
      "0.870000 0.515239 0.341351           0.173888\n",
      "0.880000 0.477586 0.316479           0.161107\n",
      "0.890000 0.439461 0.291283           0.148178\n",
      "0.900000 0.400903 0.265787           0.135115\n",
      "0.910000 0.361949 0.240018           0.121931\n",
      "0.920000 0.322637 0.213999           0.108638\n",
      "0.930000 0.283008 0.187757           0.095250\n",
      "0.940000 0.243099 0.161318           0.081781\n",
      "0.950000 0.202950 0.134707           0.068243\n",
      "0.960000 0.162601 0.107951           0.054650\n",
      "0.970000 0.122091 0.081076           0.041016\n",
      "0.980000 0.081461 0.054108           0.027354\n",
      "0.990000 0.040751 0.027074           0.013677\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.39\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.042310 0.027816           0.014494\n",
      "0.020000 0.084579 0.055618           0.028961\n",
      "0.030000 0.126764 0.083378           0.043386\n",
      "0.040000 0.168824 0.111069           0.057754\n",
      "0.050000 0.210717 0.138664           0.072053\n",
      "0.060000 0.252402 0.166136           0.086267\n",
      "0.070000 0.293839 0.193456           0.100383\n",
      "0.080000 0.334985 0.220598           0.114387\n",
      "0.090000 0.375801 0.247535           0.128266\n",
      "0.100000 0.416245 0.274240           0.142005\n",
      "0.110000 0.456279 0.300687           0.155592\n",
      "0.120000 0.495863 0.326850           0.169013\n",
      "0.130000 0.534957 0.352702           0.182256\n",
      "0.140000 0.573524 0.378217           0.195307\n",
      "0.150000 0.611524 0.403371           0.208153\n",
      "0.160000 0.648921 0.428138           0.220783\n",
      "0.170000 0.685678 0.452494           0.233184\n",
      "0.180000 0.721758 0.476414           0.245344\n",
      "0.190000 0.757125 0.499875           0.257251\n",
      "0.200000 0.791746 0.522852           0.268893\n",
      "0.210000 0.825585 0.545324           0.280261\n",
      "0.220000 0.858609 0.567267           0.291342\n",
      "0.230000 0.890786 0.588661           0.302125\n",
      "0.240000 0.922084 0.609482           0.312602\n",
      "0.250000 0.952472 0.629711           0.322760\n",
      "0.260000 0.981919 0.649328           0.332592\n",
      "0.270000 1.010398 0.668312           0.342087\n",
      "0.280000 1.037880 0.686644           0.351236\n",
      "0.290000 1.064337 0.704307           0.360031\n",
      "0.300000 1.089744 0.721282           0.368463\n",
      "0.310000 1.114076 0.737552           0.376524\n",
      "0.320000 1.137308 0.753101           0.384207\n",
      "0.330000 1.159418 0.767914           0.391504\n",
      "0.340000 1.180384 0.781974           0.398409\n",
      "0.350000 1.200184 0.795269           0.404915\n",
      "0.360000 1.218800 0.807785           0.411016\n",
      "0.370000 1.236214 0.819508           0.416706\n",
      "0.380000 1.252407 0.830427           0.421980\n",
      "0.390000 1.267365 0.840531           0.426833\n",
      "0.400000 1.281071 0.849810           0.431261\n",
      "0.410000 1.293514 0.858254           0.435260\n",
      "0.420000 1.304680 0.865853           0.438826\n",
      "0.430000 1.314558 0.872602           0.441956\n",
      "0.440000 1.323139 0.878491           0.444648\n",
      "0.450000 1.330414 0.883516           0.446898\n",
      "0.460000 1.336377 0.887671           0.448705\n",
      "0.470000 1.341020 0.890951           0.450069\n",
      "0.480000 1.344340 0.893354           0.450987\n",
      "0.490000 1.346334 0.894875           0.451459\n",
      "0.500000 1.346998 0.895513           0.451485\n",
      "0.510000 1.346334 0.895267           0.451066\n",
      "0.520000 1.344340 0.894138           0.450202\n",
      "0.530000 1.341020 0.892125           0.448895\n",
      "0.540000 1.336377 0.889231           0.447146\n",
      "0.550000 1.330414 0.885457           0.444957\n",
      "0.560000 1.323139 0.880808           0.442331\n",
      "0.570000 1.314558 0.875288           0.439270\n",
      "0.580000 1.304680 0.868900           0.435779\n",
      "0.590000 1.293514 0.861653           0.431861\n",
      "0.600000 1.281071 0.853551           0.427520\n",
      "0.610000 1.267365 0.844604           0.422761\n",
      "0.620000 1.252407 0.834819           0.417588\n",
      "0.630000 1.236214 0.824206           0.412008\n",
      "0.640000 1.218800 0.812774           0.406026\n",
      "0.650000 1.200184 0.800535           0.399649\n",
      "0.660000 1.180384 0.787501           0.392883\n",
      "0.670000 1.159418 0.773683           0.385735\n",
      "0.680000 1.137308 0.759096           0.378212\n",
      "0.690000 1.114076 0.743754           0.370323\n",
      "0.700000 1.089744 0.727670           0.362074\n",
      "0.710000 1.064337 0.710861           0.353476\n",
      "0.720000 1.037880 0.693343           0.344537\n",
      "0.730000 1.010398 0.675134           0.335265\n",
      "0.740000 0.981919 0.656249           0.325670\n",
      "0.750000 0.952472 0.636709           0.315762\n",
      "0.760000 0.922084 0.616532           0.305552\n",
      "0.770000 0.890786 0.595737           0.295049\n",
      "0.780000 0.858609 0.574345           0.284263\n",
      "0.790000 0.825585 0.552377           0.273207\n",
      "0.800000 0.791746 0.529854           0.261891\n",
      "0.810000 0.757125 0.506798           0.250327\n",
      "0.820000 0.721758 0.483232           0.238526\n",
      "0.830000 0.685678 0.459178           0.226500\n",
      "0.840000 0.648921 0.434661           0.214261\n",
      "0.850000 0.611524 0.409703           0.201821\n",
      "0.860000 0.573524 0.384330           0.189194\n",
      "0.870000 0.534957 0.358566           0.176391\n",
      "0.880000 0.495863 0.332437           0.163426\n",
      "0.890000 0.456279 0.305968           0.150311\n",
      "0.900000 0.416245 0.279186           0.137060\n",
      "0.910000 0.375801 0.252115           0.123685\n",
      "0.920000 0.334985 0.224784           0.110201\n",
      "0.930000 0.293839 0.197218           0.096620\n",
      "0.940000 0.252402 0.169445           0.082957\n",
      "0.950000 0.210717 0.141493           0.069224\n",
      "0.960000 0.168824 0.113388           0.055436\n",
      "0.970000 0.126764 0.085158           0.041605\n",
      "0.980000 0.084579 0.056832           0.027747\n",
      "0.990000 0.042310 0.028437           0.013874\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.4\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.043912 0.029222           0.014690\n",
      "0.020000 0.087780 0.058428           0.029351\n",
      "0.030000 0.131561 0.087591           0.043970\n",
      "0.040000 0.175213 0.116681           0.058532\n",
      "0.050000 0.218692 0.145669           0.073023\n",
      "0.060000 0.261955 0.174526           0.087429\n",
      "0.070000 0.304959 0.203225           0.101734\n",
      "0.080000 0.347663 0.231736           0.115927\n",
      "0.090000 0.390023 0.260031           0.129992\n",
      "0.100000 0.431999 0.288083           0.143916\n",
      "0.110000 0.473548 0.315862           0.157686\n",
      "0.120000 0.514630 0.343343           0.171287\n",
      "0.130000 0.555204 0.370496           0.184708\n",
      "0.140000 0.595230 0.397296           0.197934\n",
      "0.150000 0.634669 0.423716           0.210952\n",
      "0.160000 0.673481 0.449729           0.223752\n",
      "0.170000 0.711629 0.475310           0.236319\n",
      "0.180000 0.749074 0.500433           0.248641\n",
      "0.190000 0.785780 0.525072           0.260708\n",
      "0.200000 0.821711 0.549204           0.272506\n",
      "0.210000 0.856830 0.572805           0.284026\n",
      "0.220000 0.891105 0.595850           0.295255\n",
      "0.230000 0.924499 0.618317           0.306182\n",
      "0.240000 0.956982 0.640183           0.316799\n",
      "0.250000 0.988520 0.661426           0.327093\n",
      "0.260000 1.019082 0.682026           0.337056\n",
      "0.270000 1.048639 0.701961           0.346677\n",
      "0.280000 1.077160 0.721212           0.355949\n",
      "0.290000 1.104619 0.739758           0.364861\n",
      "0.300000 1.130988 0.757583           0.373405\n",
      "0.310000 1.156240 0.774667           0.381574\n",
      "0.320000 1.180352 0.790993           0.389359\n",
      "0.330000 1.203298 0.806545           0.396753\n",
      "0.340000 1.225057 0.821308           0.403750\n",
      "0.350000 1.245607 0.835266           0.410342\n",
      "0.360000 1.264928 0.848405           0.416523\n",
      "0.370000 1.283001 0.860712           0.422289\n",
      "0.380000 1.299807 0.872174           0.427633\n",
      "0.390000 1.315330 0.882780           0.432550\n",
      "0.400000 1.329556 0.892519           0.437037\n",
      "0.410000 1.342469 0.901381           0.441088\n",
      "0.420000 1.354058 0.909357           0.444701\n",
      "0.430000 1.364310 0.916438           0.447872\n",
      "0.440000 1.373216 0.922618           0.450598\n",
      "0.450000 1.380766 0.927889           0.452878\n",
      "0.460000 1.386954 0.932246           0.454708\n",
      "0.470000 1.391773 0.935685           0.456089\n",
      "0.480000 1.395219 0.938201           0.457018\n",
      "0.490000 1.397288 0.939792           0.457496\n",
      "0.500000 1.397978 0.940456           0.457521\n",
      "0.510000 1.397288 0.940192           0.457096\n",
      "0.520000 1.395219 0.939000           0.456219\n",
      "0.530000 1.391773 0.936880           0.454893\n",
      "0.540000 1.386954 0.933834           0.453120\n",
      "0.550000 1.380766 0.929865           0.450901\n",
      "0.560000 1.373216 0.924977           0.448239\n",
      "0.570000 1.364310 0.919173           0.445137\n",
      "0.580000 1.354058 0.912460           0.441598\n",
      "0.590000 1.342469 0.904843           0.437626\n",
      "0.600000 1.329556 0.896330           0.433226\n",
      "0.610000 1.315330 0.886928           0.428403\n",
      "0.620000 1.299807 0.876647           0.423160\n",
      "0.630000 1.283001 0.865496           0.417505\n",
      "0.640000 1.264928 0.853486           0.411442\n",
      "0.650000 1.245607 0.840628           0.404979\n",
      "0.660000 1.225057 0.826936           0.398122\n",
      "0.670000 1.203298 0.812421           0.390877\n",
      "0.680000 1.180352 0.797098           0.383254\n",
      "0.690000 1.156240 0.780982           0.375258\n",
      "0.700000 1.130988 0.764088           0.366899\n",
      "0.710000 1.104619 0.746433           0.358186\n",
      "0.720000 1.077160 0.728034           0.349126\n",
      "0.730000 1.048639 0.708908           0.339730\n",
      "0.740000 1.019082 0.689075           0.330007\n",
      "0.750000 0.988520 0.668553           0.319967\n",
      "0.760000 0.956982 0.647362           0.309620\n",
      "0.770000 0.924499 0.625523           0.298976\n",
      "0.780000 0.891105 0.603058           0.288047\n",
      "0.790000 0.856830 0.579988           0.276843\n",
      "0.800000 0.821711 0.556335           0.265375\n",
      "0.810000 0.785780 0.532123           0.253657\n",
      "0.820000 0.749074 0.507376           0.241698\n",
      "0.830000 0.711629 0.482117           0.229511\n",
      "0.840000 0.673481 0.456372           0.217109\n",
      "0.850000 0.634669 0.430165           0.204504\n",
      "0.860000 0.595230 0.403522           0.191708\n",
      "0.870000 0.555204 0.376469           0.178735\n",
      "0.880000 0.514630 0.349033           0.165597\n",
      "0.890000 0.473548 0.321240           0.152308\n",
      "0.900000 0.431999 0.293119           0.138880\n",
      "0.910000 0.390023 0.264696           0.125328\n",
      "0.920000 0.347663 0.235999           0.111664\n",
      "0.930000 0.304959 0.207056           0.097903\n",
      "0.940000 0.261955 0.177897           0.084058\n",
      "0.950000 0.218692 0.148549           0.070143\n",
      "0.960000 0.175213 0.119042           0.056171\n",
      "0.970000 0.131561 0.089404           0.042157\n",
      "0.980000 0.087780 0.059665           0.028115\n",
      "0.990000 0.043912 0.029854           0.014058\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.41000000000000003\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.045556 0.030684           0.014872\n",
      "0.020000 0.091067 0.061352           0.029715\n",
      "0.030000 0.136489 0.091974           0.044515\n",
      "0.040000 0.181775 0.122518           0.059257\n",
      "0.050000 0.226883 0.152955           0.073928\n",
      "0.060000 0.271766 0.183255           0.088511\n",
      "0.070000 0.316381 0.213387           0.102994\n",
      "0.080000 0.360684 0.243322           0.117362\n",
      "0.090000 0.404631 0.273030           0.131601\n",
      "0.100000 0.448179 0.302482           0.145697\n",
      "0.110000 0.491284 0.331648           0.159637\n",
      "0.120000 0.533905 0.360499           0.173406\n",
      "0.130000 0.575998 0.389007           0.186992\n",
      "0.140000 0.617524 0.417143           0.200381\n",
      "0.150000 0.658439 0.444879           0.213560\n",
      "0.160000 0.698705 0.472188           0.226517\n",
      "0.170000 0.738282 0.499043           0.239239\n",
      "0.180000 0.777129 0.525416           0.251713\n",
      "0.190000 0.815210 0.551282           0.263928\n",
      "0.200000 0.852487 0.576615           0.275872\n",
      "0.210000 0.888922 0.601389           0.287533\n",
      "0.220000 0.924480 0.625580           0.298900\n",
      "0.230000 0.959125 0.649163           0.309962\n",
      "0.240000 0.992824 0.672116           0.320708\n",
      "0.250000 1.025543 0.694414           0.331129\n",
      "0.260000 1.057250 0.716036           0.341214\n",
      "0.270000 1.087914 0.736960           0.350954\n",
      "0.280000 1.117504 0.757166           0.360338\n",
      "0.290000 1.145991 0.776632           0.369359\n",
      "0.300000 1.173347 0.795339           0.378008\n",
      "0.310000 1.199546 0.813269           0.386277\n",
      "0.320000 1.224560 0.830403           0.394157\n",
      "0.330000 1.248366 0.846725           0.401641\n",
      "0.340000 1.270940 0.862217           0.408723\n",
      "0.350000 1.292260 0.876864           0.415396\n",
      "0.360000 1.312304 0.890652           0.421653\n",
      "0.370000 1.331054 0.903566           0.427488\n",
      "0.380000 1.348489 0.915593           0.432897\n",
      "0.390000 1.364594 0.926721           0.437874\n",
      "0.400000 1.379353 0.936938           0.442414\n",
      "0.410000 1.392750 0.946235           0.446515\n",
      "0.420000 1.404772 0.954601           0.450171\n",
      "0.430000 1.415408 0.962028           0.453380\n",
      "0.440000 1.424648 0.968509           0.456139\n",
      "0.450000 1.432481 0.974036           0.458445\n",
      "0.460000 1.438901 0.978603           0.460298\n",
      "0.470000 1.443900 0.982206           0.461694\n",
      "0.480000 1.447475 0.984841           0.462634\n",
      "0.490000 1.449621 0.986505           0.463116\n",
      "0.500000 1.450337 0.987196           0.463141\n",
      "0.510000 1.449621 0.986912           0.462709\n",
      "0.520000 1.447475 0.985654           0.461821\n",
      "0.530000 1.443900 0.983422           0.460478\n",
      "0.540000 1.438901 0.980219           0.458682\n",
      "0.550000 1.432481 0.976046           0.456435\n",
      "0.560000 1.424648 0.970909           0.453739\n",
      "0.570000 1.415408 0.964811           0.450598\n",
      "0.580000 1.404772 0.957758           0.447014\n",
      "0.590000 1.392750 0.949756           0.442993\n",
      "0.600000 1.379353 0.940814           0.438538\n",
      "0.610000 1.364594 0.930940           0.433655\n",
      "0.620000 1.348489 0.920142           0.428347\n",
      "0.630000 1.331054 0.908432           0.422622\n",
      "0.640000 1.312304 0.895820           0.416484\n",
      "0.650000 1.292260 0.882319           0.409940\n",
      "0.660000 1.270940 0.867942           0.402998\n",
      "0.670000 1.248366 0.852702           0.395664\n",
      "0.680000 1.224560 0.836614           0.387946\n",
      "0.690000 1.199546 0.819694           0.379852\n",
      "0.700000 1.173347 0.801957           0.371390\n",
      "0.710000 1.145991 0.783422           0.362569\n",
      "0.720000 1.117504 0.764106           0.353398\n",
      "0.730000 1.087914 0.744028           0.343886\n",
      "0.740000 1.057250 0.723207           0.334043\n",
      "0.750000 1.025543 0.701664           0.323880\n",
      "0.760000 0.992824 0.679419           0.313405\n",
      "0.770000 0.959125 0.656494           0.302631\n",
      "0.780000 0.924480 0.632912           0.291567\n",
      "0.790000 0.888922 0.608696           0.280226\n",
      "0.800000 0.852487 0.583869           0.268618\n",
      "0.810000 0.815210 0.558455           0.256755\n",
      "0.820000 0.777129 0.532480           0.244650\n",
      "0.830000 0.738282 0.505968           0.232314\n",
      "0.840000 0.698705 0.478945           0.219760\n",
      "0.850000 0.658439 0.451439           0.207000\n",
      "0.860000 0.617524 0.423475           0.194048\n",
      "0.870000 0.575998 0.395082           0.180916\n",
      "0.880000 0.533905 0.366287           0.167617\n",
      "0.890000 0.491284 0.337119           0.154166\n",
      "0.900000 0.448179 0.307605           0.140574\n",
      "0.910000 0.404631 0.277775           0.126856\n",
      "0.920000 0.360684 0.247659           0.113026\n",
      "0.930000 0.316381 0.217285           0.099096\n",
      "0.940000 0.271766 0.186684           0.085082\n",
      "0.950000 0.226883 0.155885           0.070997\n",
      "0.960000 0.181775 0.124920           0.056855\n",
      "0.970000 0.136489 0.093818           0.042671\n",
      "0.980000 0.091067 0.062610           0.028457\n",
      "0.990000 0.045556 0.031327           0.014229\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.42\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.047246 0.032206           0.015040\n",
      "0.020000 0.094445 0.064393           0.030052\n",
      "0.030000 0.141551 0.096532           0.045019\n",
      "0.040000 0.188517 0.128589           0.059928\n",
      "0.050000 0.235297 0.160533           0.074764\n",
      "0.060000 0.281845 0.192333           0.089513\n",
      "0.070000 0.328115 0.223956           0.104159\n",
      "0.080000 0.374061 0.255372           0.118690\n",
      "0.090000 0.419638 0.286549           0.133089\n",
      "0.100000 0.464801 0.317457           0.147344\n",
      "0.110000 0.509505 0.348064           0.161441\n",
      "0.120000 0.553706 0.378341           0.175366\n",
      "0.130000 0.597361 0.408256           0.189105\n",
      "0.140000 0.640427 0.437782           0.202645\n",
      "0.150000 0.682860 0.466887           0.215972\n",
      "0.160000 0.724619 0.495544           0.229075\n",
      "0.170000 0.765663 0.523723           0.241940\n",
      "0.180000 0.805952 0.551398           0.254555\n",
      "0.190000 0.845445 0.578539           0.266907\n",
      "0.200000 0.884104 0.605120           0.278985\n",
      "0.210000 0.921891 0.631114           0.290777\n",
      "0.220000 0.958767 0.656496           0.302271\n",
      "0.230000 0.994698 0.681240           0.313457\n",
      "0.240000 1.029647 0.705322           0.324324\n",
      "0.250000 1.063579 0.728717           0.334862\n",
      "0.260000 1.096462 0.751402           0.345060\n",
      "0.270000 1.128263 0.773355           0.354908\n",
      "0.280000 1.158951 0.794553           0.364398\n",
      "0.290000 1.188494 0.814975           0.373520\n",
      "0.300000 1.216865 0.834600           0.382265\n",
      "0.310000 1.244035 0.853409           0.390626\n",
      "0.320000 1.269977 0.871383           0.398594\n",
      "0.330000 1.294666 0.888504           0.406162\n",
      "0.340000 1.318077 0.904755           0.413322\n",
      "0.350000 1.340188 0.920119           0.420069\n",
      "0.360000 1.360976 0.934580           0.426395\n",
      "0.370000 1.380420 0.948125           0.432296\n",
      "0.380000 1.398503 0.960739           0.437764\n",
      "0.390000 1.415205 0.972409           0.442796\n",
      "0.400000 1.430511 0.983124           0.447387\n",
      "0.410000 1.444405 0.992872           0.451532\n",
      "0.420000 1.456873 1.001645           0.455229\n",
      "0.430000 1.467904 1.009431           0.458473\n",
      "0.440000 1.477486 1.016224           0.461262\n",
      "0.450000 1.485610 1.022017           0.463593\n",
      "0.460000 1.492268 1.026803           0.465465\n",
      "0.470000 1.497453 1.030577           0.466876\n",
      "0.480000 1.501160 1.033335           0.467825\n",
      "0.490000 1.503386 1.035074           0.468312\n",
      "0.500000 1.504128 1.035792           0.468336\n",
      "0.510000 1.503386 1.035487           0.467899\n",
      "0.520000 1.501160 1.034160           0.467000\n",
      "0.530000 1.497453 1.031812           0.465640\n",
      "0.540000 1.492268 1.028445           0.463823\n",
      "0.550000 1.485610 1.024060           0.461549\n",
      "0.560000 1.477486 1.018663           0.458822\n",
      "0.570000 1.467904 1.012259           0.455645\n",
      "0.580000 1.456873 1.004852           0.452021\n",
      "0.590000 1.444405 0.996451           0.447954\n",
      "0.600000 1.430511 0.987063           0.443448\n",
      "0.610000 1.415205 0.976697           0.438509\n",
      "0.620000 1.398503 0.965362           0.433141\n",
      "0.630000 1.380420 0.953070           0.427350\n",
      "0.640000 1.360976 0.939833           0.421143\n",
      "0.650000 1.340188 0.925663           0.414525\n",
      "0.660000 1.318077 0.910573           0.407505\n",
      "0.670000 1.294666 0.894578           0.400088\n",
      "0.680000 1.269977 0.877695           0.392283\n",
      "0.690000 1.244035 0.859938           0.384097\n",
      "0.700000 1.216865 0.841325           0.375540\n",
      "0.710000 1.188494 0.821875           0.366620\n",
      "0.720000 1.158951 0.801605           0.357345\n",
      "0.730000 1.128263 0.780537           0.347726\n",
      "0.740000 1.096462 0.758689           0.337773\n",
      "0.750000 1.063579 0.736084           0.327495\n",
      "0.760000 1.029647 0.712744           0.316903\n",
      "0.770000 0.994698 0.688690           0.306008\n",
      "0.780000 0.958767 0.663947           0.294820\n",
      "0.790000 0.921891 0.638539           0.283351\n",
      "0.800000 0.884104 0.612491           0.271613\n",
      "0.810000 0.845445 0.585827           0.259618\n",
      "0.820000 0.805952 0.558575           0.247377\n",
      "0.830000 0.765663 0.530760           0.234903\n",
      "0.840000 0.724619 0.502411           0.222209\n",
      "0.850000 0.682860 0.473553           0.209306\n",
      "0.860000 0.640427 0.444217           0.196209\n",
      "0.870000 0.597361 0.414431           0.182931\n",
      "0.880000 0.553706 0.384223           0.169484\n",
      "0.890000 0.509505 0.353623           0.155882\n",
      "0.900000 0.464801 0.322663           0.142138\n",
      "0.910000 0.419638 0.291371           0.128268\n",
      "0.920000 0.374061 0.259778           0.114283\n",
      "0.930000 0.328115 0.227917           0.100199\n",
      "0.940000 0.281845 0.195817           0.086029\n",
      "0.950000 0.235297 0.163511           0.071787\n",
      "0.960000 0.188517 0.131030           0.057487\n",
      "0.970000 0.141551 0.098406           0.043145\n",
      "0.980000 0.094445 0.065672           0.028773\n",
      "0.990000 0.047246 0.032859           0.014387\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.43\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.048982 0.033787           0.015195\n",
      "0.020000 0.097916 0.067555           0.030360\n",
      "0.030000 0.146753 0.101271           0.045482\n",
      "0.040000 0.195445 0.134901           0.060544\n",
      "0.050000 0.243944 0.168412           0.075532\n",
      "0.060000 0.292203 0.201771           0.090432\n",
      "0.070000 0.340173 0.234945           0.105228\n",
      "0.080000 0.387808 0.267900           0.119907\n",
      "0.090000 0.435060 0.300605           0.134455\n",
      "0.100000 0.481882 0.333026           0.148856\n",
      "0.110000 0.528229 0.365132           0.163097\n",
      "0.120000 0.574055 0.396891           0.177164\n",
      "0.130000 0.619314 0.428271           0.191043\n",
      "0.140000 0.663962 0.459240           0.204721\n",
      "0.150000 0.707954 0.489769           0.218185\n",
      "0.160000 0.751248 0.519827           0.231422\n",
      "0.170000 0.793801 0.549383           0.244418\n",
      "0.180000 0.835570 0.578409           0.257161\n",
      "0.190000 0.876515 0.606876           0.269639\n",
      "0.200000 0.916594 0.634755           0.281840\n",
      "0.210000 0.955769 0.662018           0.293752\n",
      "0.220000 0.994001 0.688638           0.305363\n",
      "0.230000 1.031252 0.714589           0.316663\n",
      "0.240000 1.067485 0.739845           0.327641\n",
      "0.250000 1.102665 0.764380           0.338285\n",
      "0.260000 1.136756 0.788170           0.348586\n",
      "0.270000 1.169726 0.811191           0.358535\n",
      "0.280000 1.201541 0.833421           0.368120\n",
      "0.290000 1.232171 0.854836           0.377335\n",
      "0.300000 1.261584 0.875415           0.386169\n",
      "0.310000 1.289752 0.895139           0.394614\n",
      "0.320000 1.316648 0.913986           0.402662\n",
      "0.330000 1.342244 0.931938           0.410306\n",
      "0.340000 1.366516 0.948977           0.417539\n",
      "0.350000 1.389439 0.965085           0.424354\n",
      "0.360000 1.410991 0.980247           0.430744\n",
      "0.370000 1.431150 0.994447           0.436703\n",
      "0.380000 1.449897 1.007670           0.442226\n",
      "0.390000 1.467213 1.019904           0.447309\n",
      "0.400000 1.483081 1.031136           0.451945\n",
      "0.410000 1.497485 1.041354           0.456132\n",
      "0.420000 1.510412 1.050547           0.459865\n",
      "0.430000 1.521848 1.058707           0.463141\n",
      "0.440000 1.531782 1.065825           0.465957\n",
      "0.450000 1.540205 1.071893           0.468311\n",
      "0.460000 1.547107 1.076906           0.470201\n",
      "0.470000 1.552483 1.080857           0.471626\n",
      "0.480000 1.556327 1.083743           0.472584\n",
      "0.490000 1.558634 1.085560           0.473074\n",
      "0.500000 1.559404 1.086306           0.473098\n",
      "0.510000 1.558634 1.085979           0.472655\n",
      "0.520000 1.556327 1.084581           0.471745\n",
      "0.530000 1.552483 1.082111           0.470371\n",
      "0.540000 1.547107 1.078573           0.468535\n",
      "0.550000 1.540205 1.073968           0.466237\n",
      "0.560000 1.531782 1.068301           0.463481\n",
      "0.570000 1.521848 1.061578           0.460271\n",
      "0.580000 1.510412 1.053804           0.456609\n",
      "0.590000 1.497485 1.044986           0.452499\n",
      "0.600000 1.483081 1.035134           0.447947\n",
      "0.610000 1.467213 1.024257           0.442956\n",
      "0.620000 1.449897 1.012364           0.437533\n",
      "0.630000 1.431150 0.999467           0.431683\n",
      "0.640000 1.410991 0.985579           0.425412\n",
      "0.650000 1.389439 0.970713           0.418726\n",
      "0.660000 1.366516 0.954882           0.411633\n",
      "0.670000 1.342244 0.938104           0.404141\n",
      "0.680000 1.316648 0.920393           0.396255\n",
      "0.690000 1.289752 0.901766           0.387986\n",
      "0.700000 1.261584 0.882243           0.379342\n",
      "0.710000 1.232171 0.861841           0.370330\n",
      "0.720000 1.201541 0.840580           0.360961\n",
      "0.730000 1.169726 0.818482           0.351244\n",
      "0.740000 1.136756 0.795567           0.341189\n",
      "0.750000 1.102665 0.771858           0.330807\n",
      "0.760000 1.067485 0.747378           0.320107\n",
      "0.770000 1.031252 0.722152           0.309101\n",
      "0.780000 0.994001 0.696202           0.297799\n",
      "0.790000 0.955769 0.669555           0.286214\n",
      "0.800000 0.916594 0.642238           0.274357\n",
      "0.810000 0.876515 0.614275           0.262240\n",
      "0.820000 0.835570 0.585696           0.249875\n",
      "0.830000 0.793801 0.556527           0.237274\n",
      "0.840000 0.751248 0.526797           0.224451\n",
      "0.850000 0.707954 0.496536           0.211418\n",
      "0.860000 0.663962 0.465773           0.198189\n",
      "0.870000 0.619314 0.434538           0.184776\n",
      "0.880000 0.574055 0.402862           0.171193\n",
      "0.890000 0.528229 0.370776           0.157453\n",
      "0.900000 0.481882 0.338311           0.143571\n",
      "0.910000 0.435060 0.305500           0.129560\n",
      "0.920000 0.387808 0.272374           0.115434\n",
      "0.930000 0.340173 0.238965           0.101208\n",
      "0.940000 0.292203 0.205308           0.086895\n",
      "0.950000 0.243944 0.171435           0.072509\n",
      "0.960000 0.195445 0.137379           0.058066\n",
      "0.970000 0.146753 0.103174           0.043579\n",
      "0.980000 0.097916 0.068853           0.029063\n",
      "0.990000 0.048982 0.034450           0.014532\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.44\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.050767 0.035431           0.015335\n",
      "0.020000 0.101483 0.070842           0.030641\n",
      "0.030000 0.152100 0.106198           0.045902\n",
      "0.040000 0.202566 0.141463           0.061103\n",
      "0.050000 0.252832 0.176603           0.076229\n",
      "0.060000 0.302849 0.211583           0.091267\n",
      "0.070000 0.352567 0.246368           0.106199\n",
      "0.080000 0.401937 0.280923           0.121014\n",
      "0.090000 0.450911 0.315216           0.135695\n",
      "0.100000 0.499439 0.349211           0.150228\n",
      "0.110000 0.547474 0.382874           0.164600\n",
      "0.120000 0.594970 0.416173           0.178797\n",
      "0.130000 0.641878 0.449074           0.192803\n",
      "0.140000 0.688152 0.481545           0.206607\n",
      "0.150000 0.733748 0.513553           0.220195\n",
      "0.160000 0.778619 0.545067           0.233552\n",
      "0.170000 0.822722 0.576055           0.246667\n",
      "0.180000 0.866013 0.606486           0.259527\n",
      "0.190000 0.908450 0.636330           0.272120\n",
      "0.200000 0.949989 0.665557           0.284432\n",
      "0.210000 0.990592 0.694139           0.296453\n",
      "0.220000 1.030216 0.722046           0.308170\n",
      "0.230000 1.068824 0.749251           0.319573\n",
      "0.240000 1.106378 0.775727           0.330651\n",
      "0.250000 1.142839 0.801446           0.341393\n",
      "0.260000 1.178173 0.826385           0.351788\n",
      "0.270000 1.212343 0.850517           0.361827\n",
      "0.280000 1.245318 0.873818           0.371500\n",
      "0.290000 1.277063 0.896265           0.380798\n",
      "0.300000 1.307548 0.917836           0.389712\n",
      "0.310000 1.336743 0.938509           0.398233\n",
      "0.320000 1.364618 0.958263           0.406355\n",
      "0.330000 1.391147 0.977079           0.414068\n",
      "0.340000 1.416303 0.994937           0.421366\n",
      "0.350000 1.440061 1.011819           0.428242\n",
      "0.360000 1.462398 1.027708           0.434690\n",
      "0.370000 1.483292 1.042589           0.440703\n",
      "0.380000 1.502722 1.056446           0.446276\n",
      "0.390000 1.520669 1.069265           0.451404\n",
      "0.400000 1.537115 1.081033           0.456082\n",
      "0.410000 1.552044 1.091739           0.460306\n",
      "0.420000 1.565442 1.101370           0.464072\n",
      "0.430000 1.577295 1.109918           0.467377\n",
      "0.440000 1.587591 1.117373           0.470218\n",
      "0.450000 1.596320 1.123728           0.472592\n",
      "0.460000 1.603474 1.128975           0.474499\n",
      "0.470000 1.609046 1.133110           0.475935\n",
      "0.480000 1.613029 1.136129           0.476901\n",
      "0.490000 1.615421 1.138026           0.477395\n",
      "0.500000 1.616218 1.138801           0.477418\n",
      "0.510000 1.615421 1.138452           0.476969\n",
      "0.520000 1.613029 1.136979           0.476051\n",
      "0.530000 1.609046 1.134382           0.474663\n",
      "0.540000 1.603474 1.130666           0.472808\n",
      "0.550000 1.596320 1.125831           0.470489\n",
      "0.560000 1.587591 1.119884           0.467707\n",
      "0.570000 1.577295 1.112829           0.464466\n",
      "0.580000 1.565442 1.104672           0.460770\n",
      "0.590000 1.552044 1.095423           0.456622\n",
      "0.600000 1.537115 1.085088           0.452027\n",
      "0.610000 1.520669 1.073679           0.446990\n",
      "0.620000 1.502722 1.061205           0.441516\n",
      "0.630000 1.483292 1.047680           0.435612\n",
      "0.640000 1.462398 1.033115           0.429283\n",
      "0.650000 1.440061 1.017526           0.422536\n",
      "0.660000 1.416303 1.000926           0.415377\n",
      "0.670000 1.391147 0.983332           0.407816\n",
      "0.680000 1.364618 0.964760           0.399858\n",
      "0.690000 1.336743 0.945230           0.391513\n",
      "0.700000 1.307548 0.924760           0.382789\n",
      "0.710000 1.277063 0.903369           0.373694\n",
      "0.720000 1.245318 0.881078           0.364239\n",
      "0.730000 1.212343 0.857910           0.354434\n",
      "0.740000 1.178173 0.833886           0.344287\n",
      "0.750000 1.142839 0.809030           0.333809\n",
      "0.760000 1.106378 0.783366           0.323011\n",
      "0.770000 1.068824 0.756920           0.311905\n",
      "0.780000 1.030216 0.729716           0.300500\n",
      "0.790000 0.990592 0.701783           0.288809\n",
      "0.800000 0.949989 0.673145           0.276844\n",
      "0.810000 0.908450 0.643833           0.264616\n",
      "0.820000 0.866013 0.613874           0.252139\n",
      "0.830000 0.822722 0.583299           0.239424\n",
      "0.840000 0.778619 0.552135           0.226484\n",
      "0.850000 0.733748 0.520415           0.213332\n",
      "0.860000 0.688152 0.488170           0.199983\n",
      "0.870000 0.641878 0.455430           0.186448\n",
      "0.880000 0.594970 0.422228           0.172741\n",
      "0.890000 0.547474 0.388597           0.158877\n",
      "0.900000 0.499439 0.354570           0.144869\n",
      "0.910000 0.450911 0.320179           0.130731\n",
      "0.920000 0.401937 0.285460           0.116478\n",
      "0.930000 0.352567 0.250445           0.102122\n",
      "0.940000 0.302849 0.215169           0.087680\n",
      "0.950000 0.252832 0.179668           0.073164\n",
      "0.960000 0.202566 0.143975           0.058590\n",
      "0.970000 0.152100 0.108127           0.043972\n",
      "0.980000 0.101483 0.072158           0.029325\n",
      "0.990000 0.050767 0.036104           0.014663\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.45\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.052601 0.037140           0.015461\n",
      "0.020000 0.105151 0.074258           0.030893\n",
      "0.030000 0.157596 0.111318           0.046279\n",
      "0.040000 0.209887 0.148282           0.061605\n",
      "0.050000 0.261970 0.185115           0.076855\n",
      "0.060000 0.313794 0.221779           0.092015\n",
      "0.070000 0.365309 0.258238           0.107071\n",
      "0.080000 0.416463 0.294457           0.122006\n",
      "0.090000 0.467206 0.330399           0.136807\n",
      "0.100000 0.517489 0.366029           0.151460\n",
      "0.110000 0.567260 0.401311           0.165949\n",
      "0.120000 0.616472 0.436211           0.180261\n",
      "0.130000 0.665075 0.470693           0.194382\n",
      "0.140000 0.713022 0.504724           0.208299\n",
      "0.150000 0.760265 0.538269           0.221997\n",
      "0.160000 0.806758 0.571295           0.235463\n",
      "0.170000 0.852455 0.603770           0.248685\n",
      "0.180000 0.897311 0.635661           0.261650\n",
      "0.190000 0.941281 0.666937           0.274344\n",
      "0.200000 0.984322 0.697565           0.286757\n",
      "0.210000 1.026392 0.727517           0.298875\n",
      "0.220000 1.067448 0.756761           0.310688\n",
      "0.230000 1.107452 0.785269           0.322183\n",
      "0.240000 1.146362 0.813012           0.333350\n",
      "0.250000 1.184141 0.839962           0.344179\n",
      "0.260000 1.220752 0.866094           0.354658\n",
      "0.270000 1.256157 0.891379           0.364778\n",
      "0.280000 1.290323 0.915794           0.374529\n",
      "0.290000 1.323216 0.939314           0.383902\n",
      "0.300000 1.354803 0.961915           0.392888\n",
      "0.310000 1.385053 0.983574           0.401478\n",
      "0.320000 1.413936 1.004271           0.409665\n",
      "0.330000 1.441423 1.023983           0.417440\n",
      "0.340000 1.467488 1.042691           0.424797\n",
      "0.350000 1.492105 1.060377           0.431728\n",
      "0.360000 1.515249 1.077022           0.438227\n",
      "0.370000 1.536898 1.092610           0.444288\n",
      "0.380000 1.557030 1.107125           0.449905\n",
      "0.390000 1.575626 1.120552           0.455074\n",
      "0.400000 1.592666 1.132878           0.459789\n",
      "0.410000 1.608135 1.144089           0.464046\n",
      "0.420000 1.622017 1.154175           0.467842\n",
      "0.430000 1.634298 1.163126           0.471172\n",
      "0.440000 1.644966 1.170931           0.474035\n",
      "0.450000 1.654011 1.177583           0.476428\n",
      "0.460000 1.661424 1.183075           0.478349\n",
      "0.470000 1.667196 1.187400           0.479796\n",
      "0.480000 1.671324 1.190556           0.480768\n",
      "0.490000 1.673802 1.192537           0.481266\n",
      "0.500000 1.674628 1.193341           0.481287\n",
      "0.510000 1.673802 1.192968           0.480834\n",
      "0.520000 1.671324 1.191417           0.479907\n",
      "0.530000 1.667196 1.188689           0.478507\n",
      "0.540000 1.661424 1.184787           0.476637\n",
      "0.550000 1.654011 1.179714           0.474297\n",
      "0.560000 1.644966 1.173474           0.471492\n",
      "0.570000 1.634298 1.166074           0.468224\n",
      "0.580000 1.622017 1.157521           0.464496\n",
      "0.590000 1.608135 1.147821           0.460314\n",
      "0.600000 1.592666 1.136985           0.455681\n",
      "0.610000 1.575626 1.125023           0.450602\n",
      "0.620000 1.557030 1.111947           0.445084\n",
      "0.630000 1.536898 1.097768           0.439131\n",
      "0.640000 1.515249 1.082500           0.432749\n",
      "0.650000 1.492105 1.066158           0.425947\n",
      "0.660000 1.467488 1.048758           0.418730\n",
      "0.670000 1.441423 1.030317           0.411106\n",
      "0.680000 1.413936 1.010852           0.403083\n",
      "0.690000 1.385053 0.990383           0.394670\n",
      "0.700000 1.354803 0.968928           0.385874\n",
      "0.710000 1.323216 0.946510           0.376706\n",
      "0.720000 1.290323 0.923149           0.367174\n",
      "0.730000 1.256157 0.898869           0.357289\n",
      "0.740000 1.220752 0.873693           0.347059\n",
      "0.750000 1.184141 0.847645           0.336496\n",
      "0.760000 1.146362 0.820751           0.325611\n",
      "0.770000 1.107452 0.793037           0.314414\n",
      "0.780000 1.067448 0.764531           0.302917\n",
      "0.790000 1.026392 0.735260           0.291132\n",
      "0.800000 0.984322 0.705252           0.279070\n",
      "0.810000 0.941281 0.674538           0.266743\n",
      "0.820000 0.897311 0.643146           0.254165\n",
      "0.830000 0.852455 0.611108           0.241347\n",
      "0.840000 0.806758 0.578456           0.228303\n",
      "0.850000 0.760265 0.545220           0.215045\n",
      "0.860000 0.713022 0.511434           0.201588\n",
      "0.870000 0.665075 0.477131           0.187944\n",
      "0.880000 0.616472 0.442345           0.174127\n",
      "0.890000 0.567260 0.407109           0.160151\n",
      "0.900000 0.517489 0.371458           0.146031\n",
      "0.910000 0.467206 0.335427           0.131779\n",
      "0.920000 0.416463 0.299052           0.117411\n",
      "0.930000 0.365309 0.262368           0.102940\n",
      "0.940000 0.313794 0.225412           0.088382\n",
      "0.950000 0.261970 0.188219           0.073750\n",
      "0.960000 0.209887 0.150827           0.059059\n",
      "0.970000 0.157596 0.113272           0.044324\n",
      "0.980000 0.105151 0.075591           0.029560\n",
      "0.990000 0.052601 0.037821           0.014780\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.46\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.054488 0.038915           0.015573\n",
      "0.020000 0.108922 0.077807           0.031115\n",
      "0.030000 0.163249 0.116637           0.046612\n",
      "0.040000 0.217414 0.155367           0.062048\n",
      "0.050000 0.271366 0.193958           0.077408\n",
      "0.060000 0.325049 0.232372           0.092677\n",
      "0.070000 0.378411 0.270571           0.107840\n",
      "0.080000 0.431400 0.308518           0.122883\n",
      "0.090000 0.483963 0.346174           0.137790\n",
      "0.100000 0.536049 0.383502           0.152547\n",
      "0.110000 0.587606 0.420466           0.167140\n",
      "0.120000 0.638583 0.457028           0.181555\n",
      "0.130000 0.688929 0.493152           0.195777\n",
      "0.140000 0.738596 0.528803           0.209792\n",
      "0.150000 0.787533 0.563945           0.223588\n",
      "0.160000 0.835694 0.598543           0.237151\n",
      "0.170000 0.883030 0.632563           0.250467\n",
      "0.180000 0.929494 0.665971           0.263523\n",
      "0.190000 0.975041 0.698733           0.276308\n",
      "0.200000 1.019626 0.730817           0.288809\n",
      "0.210000 1.063205 0.762191           0.301013\n",
      "0.220000 1.105734 0.792824           0.312910\n",
      "0.230000 1.147172 0.822685           0.324487\n",
      "0.240000 1.187478 0.851745           0.335733\n",
      "0.250000 1.226612 0.879974           0.346638\n",
      "0.260000 1.264536 0.907344           0.357191\n",
      "0.270000 1.301211 0.933828           0.367383\n",
      "0.280000 1.336603 0.959400           0.377203\n",
      "0.290000 1.370675 0.984033           0.386642\n",
      "0.300000 1.403395 1.007704           0.395691\n",
      "0.310000 1.434730 1.030388           0.404342\n",
      "0.320000 1.464648 1.052063           0.412586\n",
      "0.330000 1.493122 1.072706           0.420415\n",
      "0.340000 1.520122 1.092298           0.427824\n",
      "0.350000 1.545621 1.110818           0.434803\n",
      "0.360000 1.569596 1.128248           0.441347\n",
      "0.370000 1.592021 1.144571           0.447450\n",
      "0.380000 1.612875 1.159769           0.453107\n",
      "0.390000 1.632138 1.173827           0.458311\n",
      "0.400000 1.649790 1.186731           0.463059\n",
      "0.410000 1.665813 1.198468           0.467345\n",
      "0.420000 1.680193 1.209026           0.471167\n",
      "0.430000 1.692914 1.218394           0.474520\n",
      "0.440000 1.703965 1.226563           0.477403\n",
      "0.450000 1.713335 1.233523           0.479811\n",
      "0.460000 1.721013 1.239268           0.481745\n",
      "0.470000 1.726993 1.243792           0.483201\n",
      "0.480000 1.731268 1.247089           0.484179\n",
      "0.490000 1.733836 1.249157           0.484679\n",
      "0.500000 1.734691 1.249992           0.484700\n",
      "0.510000 1.733836 1.249593           0.484242\n",
      "0.520000 1.731268 1.247961           0.483308\n",
      "0.530000 1.726993 1.245096           0.481897\n",
      "0.540000 1.721013 1.241001           0.480012\n",
      "0.550000 1.713335 1.235680           0.477655\n",
      "0.560000 1.703965 1.229137           0.474829\n",
      "0.570000 1.692914 1.221378           0.471536\n",
      "0.580000 1.680193 1.212411           0.467781\n",
      "0.590000 1.665813 1.202245           0.463568\n",
      "0.600000 1.649790 1.190888           0.458902\n",
      "0.610000 1.632138 1.178352           0.453786\n",
      "0.620000 1.612875 1.164648           0.448228\n",
      "0.630000 1.592021 1.149790           0.442231\n",
      "0.640000 1.569596 1.133792           0.435804\n",
      "0.650000 1.545621 1.116669           0.428953\n",
      "0.660000 1.520122 1.098438           0.421684\n",
      "0.670000 1.493122 1.079117           0.414005\n",
      "0.680000 1.464648 1.058723           0.405925\n",
      "0.690000 1.434730 1.037278           0.397452\n",
      "0.700000 1.403395 1.014801           0.388593\n",
      "0.710000 1.370675 0.991316           0.379360\n",
      "0.720000 1.336603 0.966843           0.369760\n",
      "0.730000 1.301211 0.941408           0.359804\n",
      "0.740000 1.264536 0.915034           0.349501\n",
      "0.750000 1.226612 0.887748           0.338864\n",
      "0.760000 1.187478 0.859577           0.327901\n",
      "0.770000 1.147172 0.830547           0.316625\n",
      "0.780000 1.105734 0.800688           0.305046\n",
      "0.790000 1.063205 0.770027           0.293177\n",
      "0.800000 1.019626 0.738596           0.281030\n",
      "0.810000 0.975041 0.706425           0.268616\n",
      "0.820000 0.929494 0.673545           0.255949\n",
      "0.830000 0.883030 0.639989           0.243041\n",
      "0.840000 0.835694 0.605790           0.229904\n",
      "0.850000 0.787533 0.570980           0.216553\n",
      "0.860000 0.738596 0.535595           0.203001\n",
      "0.870000 0.688929 0.499668           0.189261\n",
      "0.880000 0.638583 0.463235           0.175347\n",
      "0.890000 0.587606 0.426333           0.161273\n",
      "0.900000 0.536049 0.388996           0.147053\n",
      "0.910000 0.483963 0.351262           0.132702\n",
      "0.920000 0.431400 0.313168           0.118233\n",
      "0.930000 0.378411 0.274751           0.103661\n",
      "0.940000 0.325049 0.236049           0.089000\n",
      "0.950000 0.271366 0.197100           0.074266\n",
      "0.960000 0.217414 0.157942           0.059472\n",
      "0.970000 0.163249 0.118615           0.044634\n",
      "0.980000 0.108922 0.079156           0.029766\n",
      "0.990000 0.054488 0.039605           0.014883\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.47000000000000003\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.056428 0.040759           0.015669\n",
      "0.020000 0.112801 0.081493           0.031308\n",
      "0.030000 0.169062 0.122162           0.046900\n",
      "0.040000 0.225157 0.162725           0.062432\n",
      "0.050000 0.281029 0.203143           0.077886\n",
      "0.060000 0.336624 0.243375           0.093250\n",
      "0.070000 0.391887 0.283381           0.108506\n",
      "0.080000 0.446763 0.323122           0.123642\n",
      "0.090000 0.501198 0.362558           0.138640\n",
      "0.100000 0.555139 0.401650           0.153488\n",
      "0.110000 0.608531 0.440360           0.168171\n",
      "0.120000 0.661323 0.478649           0.182674\n",
      "0.130000 0.713463 0.516480           0.196983\n",
      "0.140000 0.764898 0.553813           0.211085\n",
      "0.150000 0.815579 0.590614           0.224965\n",
      "0.160000 0.865454 0.626844           0.238611\n",
      "0.170000 0.914476 0.662468           0.252008\n",
      "0.180000 0.962595 0.697450           0.265145\n",
      "0.190000 1.009764 0.731756           0.278008\n",
      "0.200000 1.055937 0.765352           0.290585\n",
      "0.210000 1.101067 0.798204           0.302863\n",
      "0.220000 1.145111 0.830279           0.314832\n",
      "0.230000 1.188025 0.861545           0.326479\n",
      "0.240000 1.229766 0.891972           0.337794\n",
      "0.250000 1.270294 0.921529           0.348765\n",
      "0.260000 1.309568 0.950185           0.359382\n",
      "0.270000 1.347550 0.977914           0.369636\n",
      "0.280000 1.384201 1.004687           0.379515\n",
      "0.290000 1.419487 1.030476           0.389011\n",
      "0.300000 1.453372 1.055258           0.398114\n",
      "0.310000 1.485823 1.079005           0.406817\n",
      "0.320000 1.516807 1.101696           0.415111\n",
      "0.330000 1.546294 1.123307           0.422988\n",
      "0.340000 1.574256 1.143816           0.430440\n",
      "0.350000 1.600664 1.163202           0.437461\n",
      "0.360000 1.625492 1.181447           0.444045\n",
      "0.370000 1.648716 1.198531           0.450184\n",
      "0.380000 1.670312 1.214438           0.455874\n",
      "0.390000 1.690261 1.229152           0.461109\n",
      "0.400000 1.708541 1.242657           0.465885\n",
      "0.410000 1.725136 1.254939           0.470196\n",
      "0.420000 1.740027 1.265987           0.474040\n",
      "0.430000 1.753202 1.275789           0.477413\n",
      "0.440000 1.764646 1.284334           0.480312\n",
      "0.450000 1.774349 1.291615           0.482734\n",
      "0.460000 1.782301 1.297623           0.484678\n",
      "0.470000 1.788494 1.302352           0.486142\n",
      "0.480000 1.792922 1.305796           0.487125\n",
      "0.490000 1.795580 1.307953           0.487627\n",
      "0.500000 1.796467 1.308820           0.487647\n",
      "0.510000 1.795580 1.308394           0.487186\n",
      "0.520000 1.792922 1.306677           0.486245\n",
      "0.530000 1.788494 1.303670           0.484824\n",
      "0.540000 1.782301 1.299374           0.482927\n",
      "0.550000 1.774349 1.293795           0.480554\n",
      "0.560000 1.764646 1.286937           0.477710\n",
      "0.570000 1.753202 1.278806           0.474396\n",
      "0.580000 1.740027 1.269409           0.470618\n",
      "0.590000 1.725136 1.258757           0.466378\n",
      "0.600000 1.708541 1.246859           0.461682\n",
      "0.610000 1.690261 1.233726           0.456535\n",
      "0.620000 1.670312 1.219371           0.450941\n",
      "0.630000 1.648716 1.203808           0.444908\n",
      "0.640000 1.625492 1.187051           0.438441\n",
      "0.650000 1.600664 1.169117           0.431547\n",
      "0.660000 1.574256 1.150022           0.424233\n",
      "0.670000 1.546294 1.129787           0.416508\n",
      "0.680000 1.516807 1.108429           0.408378\n",
      "0.690000 1.485823 1.085971           0.399852\n",
      "0.700000 1.453372 1.062433           0.390939\n",
      "0.710000 1.419487 1.037838           0.381649\n",
      "0.720000 1.384201 1.012211           0.371991\n",
      "0.730000 1.347550 0.985576           0.361974\n",
      "0.740000 1.309568 0.957959           0.351608\n",
      "0.750000 1.270294 0.929388           0.340906\n",
      "0.760000 1.229766 0.899890           0.329876\n",
      "0.770000 1.188025 0.869493           0.318531\n",
      "0.780000 1.145111 0.838228           0.306883\n",
      "0.790000 1.101067 0.806126           0.294942\n",
      "0.800000 1.055937 0.773216           0.282720\n",
      "0.810000 1.009764 0.739533           0.270231\n",
      "0.820000 0.962595 0.705108           0.257487\n",
      "0.830000 0.914476 0.669975           0.244501\n",
      "0.840000 0.865454 0.634169           0.231285\n",
      "0.850000 0.815579 0.597725           0.217854\n",
      "0.860000 0.764898 0.560679           0.204220\n",
      "0.870000 0.713463 0.523066           0.190397\n",
      "0.880000 0.661323 0.484925           0.176399\n",
      "0.890000 0.608531 0.446291           0.162240\n",
      "0.900000 0.555139 0.407204           0.147935\n",
      "0.910000 0.501198 0.367702           0.133497\n",
      "0.920000 0.446763 0.327822           0.118941\n",
      "0.930000 0.391887 0.287606           0.104281\n",
      "0.940000 0.336624 0.247092           0.089533\n",
      "0.950000 0.281029 0.206319           0.074710\n",
      "0.960000 0.225157 0.165329           0.059828\n",
      "0.970000 0.169062 0.124162           0.044901\n",
      "0.980000 0.112801 0.082857           0.029944\n",
      "0.990000 0.056428 0.041456           0.014972\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.48\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.058424 0.042674           0.015750\n",
      "0.020000 0.116791 0.085321           0.031470\n",
      "0.030000 0.175043 0.127900           0.047143\n",
      "0.040000 0.233122 0.170367           0.062755\n",
      "0.050000 0.290970 0.212681           0.078290\n",
      "0.060000 0.348532 0.254800           0.093732\n",
      "0.070000 0.405750 0.296682           0.109068\n",
      "0.080000 0.462567 0.338286           0.124281\n",
      "0.090000 0.518928 0.379571           0.139357\n",
      "0.100000 0.574776 0.420495           0.154282\n",
      "0.110000 0.630058 0.461018           0.169040\n",
      "0.120000 0.684717 0.501100           0.183617\n",
      "0.130000 0.738701 0.540701           0.198000\n",
      "0.140000 0.791956 0.579782           0.212174\n",
      "0.150000 0.844429 0.618304           0.226125\n",
      "0.160000 0.896069 0.656229           0.239840\n",
      "0.170000 0.946825 0.693519           0.253306\n",
      "0.180000 0.996646 0.730136           0.266510\n",
      "0.190000 1.045484 0.766045           0.279438\n",
      "0.200000 1.093289 0.801210           0.292079\n",
      "0.210000 1.140016 0.835596           0.304420\n",
      "0.220000 1.185618 0.869168           0.316450\n",
      "0.230000 1.230050 0.901894           0.328156\n",
      "0.240000 1.273268 0.933739           0.339528\n",
      "0.250000 1.315229 0.964674           0.350555\n",
      "0.260000 1.355893 0.994666           0.361226\n",
      "0.270000 1.395218 1.023687           0.371531\n",
      "0.280000 1.433166 1.051706           0.381460\n",
      "0.290000 1.469700 1.078696           0.391004\n",
      "0.300000 1.504784 1.104630           0.400153\n",
      "0.310000 1.538382 1.129483           0.408900\n",
      "0.320000 1.570463 1.153228           0.417235\n",
      "0.330000 1.600993 1.175842           0.425151\n",
      "0.340000 1.629944 1.197303           0.432641\n",
      "0.350000 1.657286 1.217589           0.439697\n",
      "0.360000 1.682992 1.236679           0.446313\n",
      "0.370000 1.707037 1.254555           0.452483\n",
      "0.380000 1.729398 1.271198           0.458201\n",
      "0.390000 1.750052 1.286591           0.463461\n",
      "0.400000 1.768979 1.300719           0.468260\n",
      "0.410000 1.786161 1.313568           0.472593\n",
      "0.420000 1.801579 1.325124           0.476455\n",
      "0.430000 1.815220 1.335376           0.479844\n",
      "0.440000 1.827069 1.344312           0.482757\n",
      "0.450000 1.837115 1.351925           0.485190\n",
      "0.460000 1.845348 1.358205           0.487143\n",
      "0.470000 1.851760 1.363146           0.488614\n",
      "0.480000 1.856345 1.366744           0.489601\n",
      "0.490000 1.859097 1.368993           0.490104\n",
      "0.500000 1.860015 1.369892           0.490123\n",
      "0.510000 1.859097 1.369439           0.489658\n",
      "0.520000 1.856345 1.367634           0.488711\n",
      "0.530000 1.851760 1.364478           0.487282\n",
      "0.540000 1.845348 1.359974           0.485374\n",
      "0.550000 1.837115 1.354126           0.482989\n",
      "0.560000 1.827069 1.346940           0.480129\n",
      "0.570000 1.815220 1.338422           0.476798\n",
      "0.580000 1.801579 1.328580           0.472999\n",
      "0.590000 1.786161 1.317424           0.468737\n",
      "0.600000 1.768979 1.304963           0.464016\n",
      "0.610000 1.750052 1.291211           0.458842\n",
      "0.620000 1.729398 1.276179           0.453219\n",
      "0.630000 1.707037 1.259883           0.447154\n",
      "0.640000 1.682992 1.242338           0.440654\n",
      "0.650000 1.657286 1.223562           0.433724\n",
      "0.660000 1.629944 1.203571           0.426372\n",
      "0.670000 1.600993 1.182386           0.418607\n",
      "0.680000 1.570463 1.160028           0.410435\n",
      "0.690000 1.538382 1.136517           0.401866\n",
      "0.700000 1.504784 1.111877           0.392907\n",
      "0.710000 1.469700 1.086131           0.383569\n",
      "0.720000 1.433166 1.059305           0.373861\n",
      "0.730000 1.395218 1.031425           0.363793\n",
      "0.740000 1.355893 1.002517           0.353375\n",
      "0.750000 1.315229 0.972611           0.342618\n",
      "0.760000 1.273268 0.941735           0.331532\n",
      "0.770000 1.230050 0.909920           0.320130\n",
      "0.780000 1.185618 0.877196           0.308422\n",
      "0.790000 1.140016 0.843596           0.296420\n",
      "0.800000 1.093289 0.809152           0.284137\n",
      "0.810000 1.045484 0.773898           0.271585\n",
      "0.820000 0.996646 0.737869           0.258777\n",
      "0.830000 0.946825 0.701100           0.245725\n",
      "0.840000 0.896069 0.663627           0.232442\n",
      "0.850000 0.844429 0.625486           0.218943\n",
      "0.860000 0.791956 0.586716           0.205240\n",
      "0.870000 0.738701 0.547353           0.191348\n",
      "0.880000 0.684717 0.507437           0.177280\n",
      "0.890000 0.630058 0.467008           0.163050\n",
      "0.900000 0.574776 0.426104           0.148673\n",
      "0.910000 0.518928 0.384765           0.134162\n",
      "0.920000 0.462567 0.343033           0.119534\n",
      "0.930000 0.405750 0.300949           0.104801\n",
      "0.940000 0.348532 0.258553           0.089979\n",
      "0.950000 0.290970 0.215889           0.075082\n",
      "0.960000 0.233122 0.172996           0.060125\n",
      "0.970000 0.175043 0.129919           0.045124\n",
      "0.980000 0.116791 0.086698           0.030093\n",
      "0.990000 0.058424 0.043378           0.015047\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.49\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.060478 0.044662           0.015816\n",
      "0.020000 0.120897 0.089295           0.031602\n",
      "0.030000 0.181196 0.133856           0.047340\n",
      "0.040000 0.241317 0.178299           0.063017\n",
      "0.050000 0.301199 0.222582           0.078617\n",
      "0.060000 0.360784 0.266660           0.094124\n",
      "0.070000 0.420013 0.310490           0.109523\n",
      "0.080000 0.478827 0.354028           0.124799\n",
      "0.090000 0.537169 0.397231           0.139938\n",
      "0.100000 0.594981 0.440057           0.154924\n",
      "0.110000 0.652206 0.482462           0.169743\n",
      "0.120000 0.708787 0.524406           0.184381\n",
      "0.130000 0.764668 0.565845           0.198823\n",
      "0.140000 0.819795 0.606740           0.213055\n",
      "0.150000 0.874113 0.647049           0.227064\n",
      "0.160000 0.927568 0.686732           0.240836\n",
      "0.170000 0.980108 0.725751           0.254357\n",
      "0.180000 1.031681 0.764066           0.267615\n",
      "0.190000 1.082235 0.801639           0.280596\n",
      "0.200000 1.131721 0.838432           0.293289\n",
      "0.210000 1.180091 0.874410           0.305681\n",
      "0.220000 1.227296 0.909536           0.317759\n",
      "0.230000 1.273289 0.943776           0.329514\n",
      "0.240000 1.318027 0.977095           0.340932\n",
      "0.250000 1.361463 1.009460           0.352003\n",
      "0.260000 1.403556 1.040838           0.362718\n",
      "0.270000 1.444263 1.071199           0.373064\n",
      "0.280000 1.483546 1.100512           0.383033\n",
      "0.290000 1.521364 1.128748           0.392616\n",
      "0.300000 1.557681 1.155879           0.401802\n",
      "0.310000 1.592460 1.181877           0.410583\n",
      "0.320000 1.625668 1.206716           0.418952\n",
      "0.330000 1.657272 1.230372           0.426900\n",
      "0.340000 1.687240 1.252821           0.434419\n",
      "0.350000 1.715543 1.274040           0.441503\n",
      "0.360000 1.742153 1.294008           0.448146\n",
      "0.370000 1.767044 1.312704           0.454340\n",
      "0.380000 1.790191 1.330111           0.460080\n",
      "0.390000 1.811571 1.346210           0.465362\n",
      "0.400000 1.831164 1.360985           0.470179\n",
      "0.410000 1.848949 1.374421           0.474528\n",
      "0.420000 1.864909 1.386504           0.478406\n",
      "0.430000 1.879029 1.397222           0.481807\n",
      "0.440000 1.891295 1.406564           0.484731\n",
      "0.450000 1.901694 1.414521           0.487173\n",
      "0.460000 1.910217 1.421084           0.489133\n",
      "0.470000 1.916854 1.426246           0.490609\n",
      "0.480000 1.921600 1.430001           0.491599\n",
      "0.490000 1.924449 1.432347           0.492103\n",
      "0.500000 1.925399 1.433279           0.492121\n",
      "0.510000 1.924449 1.432796           0.491653\n",
      "0.520000 1.921600 1.430899           0.490701\n",
      "0.530000 1.916854 1.427589           0.489265\n",
      "0.540000 1.910217 1.422869           0.487348\n",
      "0.550000 1.901694 1.416742           0.484952\n",
      "0.560000 1.891295 1.409216           0.482080\n",
      "0.570000 1.879029 1.400296           0.478734\n",
      "0.580000 1.864909 1.389991           0.474919\n",
      "0.590000 1.848949 1.378310           0.470638\n",
      "0.600000 1.831164 1.365266           0.465897\n",
      "0.610000 1.811571 1.350870           0.460701\n",
      "0.620000 1.790191 1.335136           0.455055\n",
      "0.630000 1.767044 1.318080           0.448964\n",
      "0.640000 1.742153 1.299717           0.442436\n",
      "0.650000 1.715543 1.280066           0.435478\n",
      "0.660000 1.687240 1.259145           0.428095\n",
      "0.670000 1.657272 1.236975           0.420298\n",
      "0.680000 1.625668 1.213577           0.412092\n",
      "0.690000 1.592460 1.188973           0.403487\n",
      "0.700000 1.557681 1.163189           0.394492\n",
      "0.710000 1.521364 1.136249           0.385115\n",
      "0.720000 1.483546 1.108178           0.375367\n",
      "0.730000 1.444263 1.079005           0.365258\n",
      "0.740000 1.403556 1.048759           0.354797\n",
      "0.750000 1.361463 1.017467           0.343996\n",
      "0.760000 1.318027 0.985161           0.332865\n",
      "0.770000 1.273289 0.951873           0.321416\n",
      "0.780000 1.227296 0.917635           0.309660\n",
      "0.790000 1.180091 0.882481           0.297610\n",
      "0.800000 1.131721 0.846444           0.285277\n",
      "0.810000 1.082235 0.809561           0.272674\n",
      "0.820000 1.031681 0.771867           0.259813\n",
      "0.830000 0.980108 0.733399           0.246709\n",
      "0.840000 0.927568 0.694196           0.233373\n",
      "0.850000 0.874113 0.654294           0.219819\n",
      "0.860000 0.819795 0.613734           0.206061\n",
      "0.870000 0.764668 0.572556           0.192112\n",
      "0.880000 0.708787 0.530799           0.177988\n",
      "0.890000 0.652206 0.488505           0.163701\n",
      "0.900000 0.594981 0.445715           0.149266\n",
      "0.910000 0.537169 0.402472           0.134697\n",
      "0.920000 0.478827 0.358817           0.120010\n",
      "0.930000 0.420013 0.314795           0.105218\n",
      "0.940000 0.360784 0.270447           0.090337\n",
      "0.950000 0.301199 0.225818           0.075381\n",
      "0.960000 0.241317 0.180952           0.060364\n",
      "0.970000 0.181196 0.135893           0.045303\n",
      "0.980000 0.120897 0.090684           0.030212\n",
      "0.990000 0.060478 0.045372           0.015106\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.5\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.062592 0.046725           0.015867\n",
      "0.020000 0.125122 0.093419           0.031702\n",
      "0.030000 0.187528 0.140037           0.047491\n",
      "0.040000 0.249750 0.186532           0.063218\n",
      "0.050000 0.311724 0.232858           0.078866\n",
      "0.060000 0.373392 0.278969           0.094422\n",
      "0.070000 0.434691 0.324820           0.109870\n",
      "0.080000 0.495560 0.370366           0.125195\n",
      "0.090000 0.555941 0.415560           0.140381\n",
      "0.100000 0.615773 0.460359           0.155414\n",
      "0.110000 0.674998 0.504718           0.170280\n",
      "0.120000 0.733556 0.548592           0.184964\n",
      "0.130000 0.791390 0.591939           0.199451\n",
      "0.140000 0.848444 0.634716           0.213728\n",
      "0.150000 0.904660 0.676879           0.227780\n",
      "0.160000 0.959983 0.718388           0.241595\n",
      "0.170000 1.014359 0.759201           0.255158\n",
      "0.180000 1.067734 0.799277           0.268457\n",
      "0.190000 1.120055 0.838576           0.281479\n",
      "0.200000 1.171270 0.877060           0.294211\n",
      "0.210000 1.221330 0.914690           0.306640\n",
      "0.220000 1.270185 0.951428           0.318756\n",
      "0.230000 1.317786 0.987239           0.330547\n",
      "0.240000 1.364086 1.022086           0.342000\n",
      "0.250000 1.409040 1.055935           0.353105\n",
      "0.260000 1.452604 1.088752           0.363852\n",
      "0.270000 1.494734 1.120504           0.374230\n",
      "0.280000 1.535389 1.151160           0.384230\n",
      "0.290000 1.574529 1.180688           0.393841\n",
      "0.300000 1.612115 1.209060           0.403055\n",
      "0.310000 1.648110 1.236247           0.411863\n",
      "0.320000 1.682479 1.262222           0.420257\n",
      "0.330000 1.715187 1.286958           0.428229\n",
      "0.340000 1.746202 1.310432           0.435771\n",
      "0.350000 1.775495 1.332619           0.442876\n",
      "0.360000 1.803034 1.353497           0.449538\n",
      "0.370000 1.828795 1.373045           0.455750\n",
      "0.380000 1.852751 1.391244           0.461507\n",
      "0.390000 1.874878 1.408074           0.466804\n",
      "0.400000 1.895155 1.423520           0.471635\n",
      "0.410000 1.913562 1.437565           0.475997\n",
      "0.420000 1.930080 1.450195           0.479885\n",
      "0.430000 1.944694 1.461397           0.483297\n",
      "0.440000 1.957388 1.471160           0.486228\n",
      "0.450000 1.968151 1.479474           0.488677\n",
      "0.460000 1.976971 1.486329           0.490642\n",
      "0.470000 1.983840 1.491720           0.492121\n",
      "0.480000 1.988752 1.495639           0.493113\n",
      "0.490000 1.991701 1.498084           0.493617\n",
      "0.500000 1.992684 1.499050           0.493634\n",
      "0.510000 1.991701 1.498536           0.493164\n",
      "0.520000 1.988752 1.496544           0.492208\n",
      "0.530000 1.983840 1.493073           0.490767\n",
      "0.540000 1.976971 1.488128           0.488843\n",
      "0.550000 1.968151 1.481712           0.486439\n",
      "0.560000 1.957388 1.473832           0.483556\n",
      "0.570000 1.944694 1.464495           0.480199\n",
      "0.580000 1.930080 1.453709           0.476371\n",
      "0.590000 1.913562 1.441485           0.472077\n",
      "0.600000 1.895155 1.427835           0.467320\n",
      "0.610000 1.874878 1.412771           0.462107\n",
      "0.620000 1.852751 1.396308           0.456443\n",
      "0.630000 1.828795 1.378462           0.450333\n",
      "0.640000 1.803034 1.359251           0.443784\n",
      "0.650000 1.775495 1.338692           0.436803\n",
      "0.660000 1.746202 1.316805           0.429397\n",
      "0.670000 1.715187 1.293612           0.421575\n",
      "0.680000 1.682479 1.269135           0.413343\n",
      "0.690000 1.648110 1.243399           0.404711\n",
      "0.700000 1.612115 1.216427           0.395688\n",
      "0.710000 1.574529 1.188247           0.386282\n",
      "0.720000 1.535389 1.158885           0.376504\n",
      "0.730000 1.494734 1.128371           0.366363\n",
      "0.740000 1.452604 1.096734           0.355870\n",
      "0.750000 1.409040 1.064005           0.345035\n",
      "0.760000 1.364086 1.030216           0.333870\n",
      "0.770000 1.317786 0.995400           0.322386\n",
      "0.780000 1.270185 0.959591           0.310594\n",
      "0.790000 1.221330 0.922823           0.298507\n",
      "0.800000 1.171270 0.885134           0.286136\n",
      "0.810000 1.120055 0.846560           0.273494\n",
      "0.820000 1.067734 0.807139           0.260595\n",
      "0.830000 1.014359 0.766909           0.247450\n",
      "0.840000 0.959983 0.725910           0.234073\n",
      "0.850000 0.904660 0.684181           0.220478\n",
      "0.860000 0.848444 0.641765           0.206679\n",
      "0.870000 0.791390 0.598702           0.192688\n",
      "0.880000 0.733556 0.555035           0.178521\n",
      "0.890000 0.674998 0.510807           0.164190\n",
      "0.900000 0.615773 0.466061           0.149712\n",
      "0.910000 0.555941 0.420841           0.135100\n",
      "0.920000 0.495560 0.375192           0.120368\n",
      "0.930000 0.434691 0.329159           0.105532\n",
      "0.940000 0.373392 0.282786           0.090606\n",
      "0.950000 0.311724 0.236119           0.075605\n",
      "0.960000 0.249750 0.189205           0.060544\n",
      "0.970000 0.187528 0.142090           0.045438\n",
      "0.980000 0.125122 0.094820           0.030302\n",
      "0.990000 0.062592 0.047441           0.015151\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.51\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.064767 0.048866           0.015901\n",
      "0.020000 0.129470 0.097699           0.031771\n",
      "0.030000 0.194045 0.146451           0.047595\n",
      "0.040000 0.258429 0.195074           0.063355\n",
      "0.050000 0.322558 0.243520           0.079038\n",
      "0.060000 0.386368 0.291741           0.094628\n",
      "0.070000 0.449797 0.339689           0.110109\n",
      "0.080000 0.512783 0.387316           0.125466\n",
      "0.090000 0.575262 0.434577           0.140685\n",
      "0.100000 0.637173 0.481423           0.155751\n",
      "0.110000 0.698456 0.527808           0.170648\n",
      "0.120000 0.759049 0.573686           0.185363\n",
      "0.130000 0.818893 0.619012           0.199881\n",
      "0.140000 0.877930 0.663741           0.214188\n",
      "0.150000 0.936099 0.707829           0.228270\n",
      "0.160000 0.993345 0.751231           0.242114\n",
      "0.170000 1.049611 0.793905           0.255706\n",
      "0.180000 1.104840 0.835808           0.269033\n",
      "0.190000 1.158980 0.876898           0.282082\n",
      "0.200000 1.211975 0.917135           0.294840\n",
      "0.210000 1.263775 0.956479           0.307296\n",
      "0.220000 1.314327 0.994890           0.319437\n",
      "0.230000 1.363583 1.032331           0.331252\n",
      "0.240000 1.411492 1.068763           0.342729\n",
      "0.250000 1.458009 1.104152           0.353857\n",
      "0.260000 1.503086 1.138460           0.364626\n",
      "0.270000 1.546681 1.171655           0.375026\n",
      "0.280000 1.588749 1.203703           0.385045\n",
      "0.290000 1.629249 1.234573           0.394676\n",
      "0.300000 1.668141 1.264232           0.403909\n",
      "0.310000 1.705387 1.292652           0.412735\n",
      "0.320000 1.740950 1.319804           0.421145\n",
      "0.330000 1.774795 1.345662           0.429133\n",
      "0.340000 1.806888 1.370198           0.436690\n",
      "0.350000 1.837198 1.393389           0.443809\n",
      "0.360000 1.865695 1.415211           0.450484\n",
      "0.370000 1.892351 1.435643           0.456708\n",
      "0.380000 1.917139 1.454663           0.462477\n",
      "0.390000 1.940036 1.472252           0.467784\n",
      "0.400000 1.961017 1.488393           0.472624\n",
      "0.410000 1.980064 1.503070           0.476994\n",
      "0.420000 1.997156 1.516267           0.480889\n",
      "0.430000 2.012278 1.527971           0.484307\n",
      "0.440000 2.025413 1.538170           0.487243\n",
      "0.450000 2.036550 1.546854           0.489696\n",
      "0.460000 2.045677 1.554013           0.491664\n",
      "0.470000 2.052785 1.559640           0.493145\n",
      "0.480000 2.057867 1.563729           0.494138\n",
      "0.490000 2.060918 1.566276           0.494642\n",
      "0.500000 2.061936 1.567277           0.494658\n",
      "0.510000 2.060918 1.566732           0.494186\n",
      "0.520000 2.057867 1.564640           0.493227\n",
      "0.530000 2.052785 1.561003           0.491782\n",
      "0.540000 2.045677 1.555824           0.489853\n",
      "0.550000 2.036550 1.549107           0.487443\n",
      "0.560000 2.025413 1.540860           0.484553\n",
      "0.570000 2.012278 1.531089           0.481188\n",
      "0.580000 1.997156 1.519805           0.477351\n",
      "0.590000 1.980064 1.507017           0.473047\n",
      "0.600000 1.961017 1.492737           0.468280\n",
      "0.610000 1.940036 1.476981           0.463055\n",
      "0.620000 1.917139 1.459762           0.457378\n",
      "0.630000 1.892351 1.441097           0.451254\n",
      "0.640000 1.865695 1.421004           0.444691\n",
      "0.650000 1.837198 1.399503           0.437695\n",
      "0.660000 1.806888 1.376614           0.430274\n",
      "0.670000 1.774795 1.352361           0.422434\n",
      "0.680000 1.740950 1.326765           0.414185\n",
      "0.690000 1.705387 1.299852           0.405535\n",
      "0.700000 1.668141 1.271649           0.396492\n",
      "0.710000 1.629249 1.242182           0.387066\n",
      "0.720000 1.588749 1.211481           0.377267\n",
      "0.730000 1.546681 1.179576           0.367105\n",
      "0.740000 1.503086 1.146496           0.356590\n",
      "0.750000 1.458009 1.112276           0.345733\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.760000 1.411492 1.076948           0.334544\n",
      "0.770000 1.363583 1.040546           0.323036\n",
      "0.780000 1.314327 1.003108           0.311220\n",
      "0.790000 1.263775 0.964668           0.299107\n",
      "0.800000 1.211975 0.925264           0.286711\n",
      "0.810000 1.158980 0.884936           0.274043\n",
      "0.820000 1.104840 0.843723           0.261117\n",
      "0.830000 1.049611 0.801665           0.247946\n",
      "0.840000 0.993345 0.758803           0.234542\n",
      "0.850000 0.936099 0.715180           0.220919\n",
      "0.860000 0.877930 0.670838           0.207091\n",
      "0.870000 0.818893 0.625821           0.193072\n",
      "0.880000 0.759049 0.580173           0.178876\n",
      "0.890000 0.698456 0.533939           0.164517\n",
      "0.900000 0.637173 0.487164           0.150010\n",
      "0.910000 0.575262 0.439894           0.135368\n",
      "0.920000 0.512783 0.392176           0.120607\n",
      "0.930000 0.449797 0.344056           0.105741\n",
      "0.940000 0.386368 0.295583           0.090785\n",
      "0.950000 0.322558 0.246803           0.075755\n",
      "0.960000 0.258429 0.197765           0.060664\n",
      "0.970000 0.194045 0.148517           0.045528\n",
      "0.980000 0.129470 0.099108           0.030362\n",
      "0.990000 0.064767 0.049586           0.015181\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.52\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.067006 0.051086           0.015920\n",
      "0.020000 0.133946 0.102137           0.031809\n",
      "0.030000 0.200754 0.153104           0.047650\n",
      "0.040000 0.267364 0.203934           0.063429\n",
      "0.050000 0.333710 0.254579           0.079130\n",
      "0.060000 0.399726 0.304988           0.094738\n",
      "0.070000 0.465348 0.355111           0.110237\n",
      "0.080000 0.530511 0.404899           0.125612\n",
      "0.090000 0.595150 0.454302           0.140848\n",
      "0.100000 0.659202 0.503271           0.155931\n",
      "0.110000 0.722603 0.551758           0.170845\n",
      "0.120000 0.785292 0.599715           0.185577\n",
      "0.130000 0.847205 0.647094           0.200111\n",
      "0.140000 0.908282 0.693848           0.214434\n",
      "0.150000 0.968463 0.739931           0.228532\n",
      "0.160000 1.027688 0.785297           0.242391\n",
      "0.170000 1.085899 0.829901           0.255998\n",
      "0.180000 1.143038 0.873698           0.269339\n",
      "0.190000 1.199049 0.916646           0.282403\n",
      "0.200000 1.253877 0.958702           0.295175\n",
      "0.210000 1.307467 0.999823           0.307644\n",
      "0.220000 1.359767 1.039969           0.319799\n",
      "0.230000 1.410725 1.079100           0.331626\n",
      "0.240000 1.460291 1.117176           0.343115\n",
      "0.250000 1.508416 1.154161           0.354255\n",
      "0.260000 1.555052 1.190017           0.365035\n",
      "0.270000 1.600154 1.224708           0.375446\n",
      "0.280000 1.643676 1.258200           0.385476\n",
      "0.290000 1.685576 1.290460           0.395117\n",
      "0.300000 1.725813 1.321454           0.404359\n",
      "0.310000 1.764347 1.351153           0.413194\n",
      "0.320000 1.801139 1.379527           0.421613\n",
      "0.330000 1.836154 1.406546           0.429608\n",
      "0.340000 1.869357 1.432185           0.437172\n",
      "0.350000 1.900715 1.456417           0.444298\n",
      "0.360000 1.930197 1.479218           0.450980\n",
      "0.370000 1.957775 1.500565           0.457210\n",
      "0.380000 1.983420 1.520436           0.462984\n",
      "0.390000 2.007108 1.538813           0.468295\n",
      "0.400000 2.028815 1.555675           0.473140\n",
      "0.410000 2.048520 1.571006           0.477514\n",
      "0.420000 2.066203 1.584791           0.481412\n",
      "0.430000 2.081848 1.597015           0.484832\n",
      "0.440000 2.095437 1.607666           0.487771\n",
      "0.450000 2.106959 1.616733           0.490226\n",
      "0.460000 2.116401 1.624207           0.492194\n",
      "0.470000 2.123755 1.630079           0.493676\n",
      "0.480000 2.129013 1.634344           0.494669\n",
      "0.490000 2.132170 1.636997           0.495173\n",
      "0.500000 2.133223 1.638035           0.495188\n",
      "0.510000 2.132170 1.637456           0.494714\n",
      "0.520000 2.129013 1.635260           0.493753\n",
      "0.530000 2.123755 1.631450           0.492305\n",
      "0.540000 2.116401 1.626028           0.490373\n",
      "0.550000 2.106959 1.619000           0.487959\n",
      "0.560000 2.095437 1.610372           0.485066\n",
      "0.570000 2.081848 1.600152           0.481696\n",
      "0.580000 2.066203 1.588349           0.477854\n",
      "0.590000 2.048520 1.574976           0.473544\n",
      "0.600000 2.028815 1.560044           0.468771\n",
      "0.610000 2.007108 1.543568           0.463540\n",
      "0.620000 1.983420 1.525564           0.457856\n",
      "0.630000 1.957775 1.506050           0.451725\n",
      "0.640000 1.930197 1.485043           0.445154\n",
      "0.650000 1.900715 1.462565           0.438150\n",
      "0.660000 1.869357 1.438638           0.430719\n",
      "0.670000 1.836154 1.413283           0.422871\n",
      "0.680000 1.801139 1.386527           0.414612\n",
      "0.690000 1.764347 1.358395           0.405952\n",
      "0.700000 1.725813 1.328914           0.396900\n",
      "0.710000 1.685576 1.298113           0.387463\n",
      "0.720000 1.643676 1.266023           0.377654\n",
      "0.730000 1.600154 1.232674           0.367480\n",
      "0.740000 1.555052 1.198099           0.356954\n",
      "0.750000 1.508416 1.162332           0.346084\n",
      "0.760000 1.460291 1.125407           0.334884\n",
      "0.770000 1.410725 1.087362           0.323363\n",
      "0.780000 1.359767 1.048233           0.311534\n",
      "0.790000 1.307467 1.008058           0.299409\n",
      "0.800000 1.253877 0.966877           0.287000\n",
      "0.810000 1.199049 0.924730           0.274319\n",
      "0.820000 1.143038 0.881659           0.261379\n",
      "0.830000 1.085899 0.837705           0.248194\n",
      "0.840000 1.027688 0.792912           0.234776\n",
      "0.850000 0.968463 0.747324           0.221139\n",
      "0.860000 0.908282 0.700985           0.207297\n",
      "0.870000 0.847205 0.653941           0.193264\n",
      "0.880000 0.785292 0.606238           0.179053\n",
      "0.890000 0.722603 0.557924           0.164680\n",
      "0.900000 0.659202 0.509045           0.150157\n",
      "0.910000 0.595150 0.459649           0.135501\n",
      "0.920000 0.530511 0.409786           0.120725\n",
      "0.930000 0.465348 0.359504           0.105845\n",
      "0.940000 0.399726 0.308852           0.090874\n",
      "0.950000 0.333710 0.257881           0.075828\n",
      "0.960000 0.267364 0.206641           0.060723\n",
      "0.970000 0.200754 0.155182           0.045572\n",
      "0.980000 0.133946 0.103555           0.030391\n",
      "0.990000 0.067006 0.051811           0.015196\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.53\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.069311 0.053389           0.015923\n",
      "0.020000 0.138554 0.106740           0.031814\n",
      "0.030000 0.207661 0.160003           0.047658\n",
      "0.040000 0.276562 0.213122           0.063440\n",
      "0.050000 0.345191 0.266048           0.079143\n",
      "0.060000 0.413478 0.318725           0.094753\n",
      "0.070000 0.481358 0.371104           0.110254\n",
      "0.080000 0.548763 0.423132           0.125631\n",
      "0.090000 0.615626 0.474756           0.140870\n",
      "0.100000 0.681882 0.525927           0.155954\n",
      "0.110000 0.747464 0.576594           0.170870\n",
      "0.120000 0.812309 0.626706           0.185604\n",
      "0.130000 0.876352 0.676213           0.200139\n",
      "0.140000 0.939531 0.725067           0.214464\n",
      "0.150000 1.001782 0.773219           0.228563\n",
      "0.160000 1.063045 0.820621           0.242424\n",
      "0.170000 1.123258 0.867226           0.256032\n",
      "0.180000 1.182363 0.912989           0.269375\n",
      "0.190000 1.240302 0.957863           0.282439\n",
      "0.200000 1.297016 1.001803           0.295212\n",
      "0.210000 1.352450 1.044767           0.307682\n",
      "0.220000 1.406549 1.086712           0.319837\n",
      "0.230000 1.459261 1.127595           0.331665\n",
      "0.240000 1.510532 1.167377           0.343155\n",
      "0.250000 1.560312 1.206016           0.354296\n",
      "0.260000 1.608553 1.243476           0.365077\n",
      "0.270000 1.655206 1.279719           0.375487\n",
      "0.280000 1.700226 1.314708           0.385518\n",
      "0.290000 1.743568 1.348409           0.395159\n",
      "0.300000 1.785189 1.380788           0.404401\n",
      "0.310000 1.825048 1.411813           0.413236\n",
      "0.320000 1.863107 1.441452           0.421655\n",
      "0.330000 1.899326 1.469676           0.429650\n",
      "0.340000 1.933671 1.496457           0.437214\n",
      "0.350000 1.966108 1.521768           0.444340\n",
      "0.360000 1.996605 1.545584           0.451021\n",
      "0.370000 2.025131 1.567880           0.457251\n",
      "0.380000 2.051659 1.588635           0.463024\n",
      "0.390000 2.076162 1.607826           0.468335\n",
      "0.400000 2.098615 1.625436           0.473179\n",
      "0.410000 2.118998 1.641446           0.477552\n",
      "0.420000 2.137290 1.655840           0.481450\n",
      "0.430000 2.153472 1.668603           0.484869\n",
      "0.440000 2.167530 1.679723           0.487807\n",
      "0.450000 2.179448 1.689187           0.490261\n",
      "0.460000 2.189215 1.696986           0.492229\n",
      "0.470000 2.196822 1.703112           0.493709\n",
      "0.480000 2.202261 1.707559           0.494701\n",
      "0.490000 2.205526 1.710322           0.495204\n",
      "0.500000 2.206615 1.711396           0.495218\n",
      "0.510000 2.205526 1.710782           0.494744\n",
      "0.520000 2.202261 1.708479           0.493781\n",
      "0.530000 2.196822 1.704489           0.492333\n",
      "0.540000 2.189215 1.698816           0.490399\n",
      "0.550000 2.179448 1.691464           0.487984\n",
      "0.560000 2.167530 1.682440           0.485089\n",
      "0.570000 2.153472 1.671754           0.481719\n",
      "0.580000 2.137290 1.659414           0.477876\n",
      "0.590000 2.118998 1.645434           0.473565\n",
      "0.600000 2.098615 1.629825           0.468790\n",
      "0.610000 2.076162 1.612604           0.463557\n",
      "0.620000 2.051659 1.593786           0.457872\n",
      "0.630000 2.025131 1.573391           0.451740\n",
      "0.640000 1.996605 1.551437           0.445168\n",
      "0.650000 1.966108 1.527946           0.438163\n",
      "0.660000 1.933671 1.502940           0.430731\n",
      "0.670000 1.899326 1.476444           0.422882\n",
      "0.680000 1.863107 1.448484           0.414622\n",
      "0.690000 1.825048 1.419087           0.405961\n",
      "0.700000 1.785189 1.388282           0.396907\n",
      "0.710000 1.743568 1.356098           0.387470\n",
      "0.720000 1.700226 1.322567           0.377659\n",
      "0.730000 1.655206 1.287721           0.367485\n",
      "0.740000 1.608553 1.251596           0.356957\n",
      "0.750000 1.560312 1.214225           0.346087\n",
      "0.760000 1.510532 1.175646           0.334886\n",
      "0.770000 1.459261 1.135896           0.323365\n",
      "0.780000 1.406549 1.095014           0.311535\n",
      "0.790000 1.352450 1.053041           0.299409\n",
      "0.800000 1.297016 1.010017           0.286999\n",
      "0.810000 1.240302 0.965984           0.274318\n",
      "0.820000 1.182363 0.920986           0.261377\n",
      "0.830000 1.123258 0.875067           0.248192\n",
      "0.840000 1.063045 0.828272           0.234773\n",
      "0.850000 1.001782 0.780646           0.221136\n",
      "0.860000 0.939531 0.732237           0.207294\n",
      "0.870000 0.876352 0.683092           0.193261\n",
      "0.880000 0.812309 0.633259           0.179050\n",
      "0.890000 0.747464 0.582788           0.164676\n",
      "0.900000 0.681882 0.531728           0.150154\n",
      "0.910000 0.615626 0.480128           0.135498\n",
      "0.920000 0.548763 0.428041           0.120722\n",
      "0.930000 0.481358 0.375517           0.105841\n",
      "0.940000 0.413478 0.322607           0.090871\n",
      "0.950000 0.345191 0.269365           0.075826\n",
      "0.960000 0.276562 0.215842           0.060720\n",
      "0.970000 0.207661 0.162091           0.045570\n",
      "0.980000 0.138554 0.108164           0.030390\n",
      "0.990000 0.069311 0.054117           0.015195\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.54\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.071685 0.055776           0.015909\n",
      "0.020000 0.143300 0.111513           0.031787\n",
      "0.030000 0.214773 0.167155           0.047618\n",
      "0.040000 0.286034 0.222648           0.063386\n",
      "0.050000 0.357012 0.277937           0.079075\n",
      "0.060000 0.427639 0.332967           0.094672\n",
      "0.070000 0.497843 0.387684           0.110159\n",
      "0.080000 0.567556 0.442034           0.125523\n",
      "0.090000 0.636709 0.495962           0.140748\n",
      "0.100000 0.705234 0.549415           0.155819\n",
      "0.110000 0.773063 0.602341           0.170722\n",
      "0.120000 0.840128 0.654687           0.185442\n",
      "0.130000 0.906365 0.706401           0.199964\n",
      "0.140000 0.971707 0.757431           0.214276\n",
      "0.150000 1.036090 0.807728           0.228362\n",
      "0.160000 1.099451 0.857241           0.242210\n",
      "0.170000 1.161727 0.905921           0.255806\n",
      "0.180000 1.222856 0.953720           0.269136\n",
      "0.190000 1.282778 1.000590           0.282188\n",
      "0.200000 1.341435 1.046485           0.294950\n",
      "0.210000 1.398767 1.091360           0.307408\n",
      "0.220000 1.454720 1.135168           0.319551\n",
      "0.230000 1.509236 1.177868           0.331368\n",
      "0.240000 1.562263 1.219417           0.342847\n",
      "0.250000 1.613749 1.259772           0.353977\n",
      "0.260000 1.663642 1.298895           0.364747\n",
      "0.270000 1.711892 1.336745           0.375147\n",
      "0.280000 1.758454 1.373286           0.385168\n",
      "0.290000 1.803280 1.408481           0.394799\n",
      "0.300000 1.846327 1.442295           0.404032\n",
      "0.310000 1.887551 1.474693           0.412858\n",
      "0.320000 1.926913 1.505644           0.421268\n",
      "0.330000 1.964373 1.535117           0.429255\n",
      "0.340000 1.999894 1.563083           0.436812\n",
      "0.350000 2.033442 1.589512           0.443930\n",
      "0.360000 2.064983 1.614379           0.450604\n",
      "0.370000 2.094486 1.637659           0.456827\n",
      "0.380000 2.121922 1.659328           0.462594\n",
      "0.390000 2.147264 1.679365           0.467899\n",
      "0.400000 2.170487 1.697750           0.472738\n",
      "0.410000 2.191568 1.714463           0.477106\n",
      "0.420000 2.210486 1.729488           0.480999\n",
      "0.430000 2.227223 1.742809           0.484414\n",
      "0.440000 2.241762 1.754414           0.487348\n",
      "0.450000 2.254088 1.764290           0.489798\n",
      "0.460000 2.264190 1.772426           0.491763\n",
      "0.470000 2.272057 1.778816           0.493241\n",
      "0.480000 2.277682 1.783451           0.494231\n",
      "0.490000 2.281059 1.786326           0.494733\n",
      "0.500000 2.282185 1.787439           0.494746\n",
      "0.510000 2.281059 1.786789           0.494271\n",
      "0.520000 2.277682 1.784374           0.493308\n",
      "0.530000 2.272057 1.780197           0.491860\n",
      "0.540000 2.264190 1.774262           0.489927\n",
      "0.550000 2.254088 1.766575           0.487513\n",
      "0.560000 2.241762 1.757141           0.484620\n",
      "0.570000 2.227223 1.745971           0.481252\n",
      "0.580000 2.210486 1.733075           0.477412\n",
      "0.590000 2.191568 1.718464           0.473104\n",
      "0.600000 2.170487 1.702154           0.468333\n",
      "0.610000 2.147264 1.684160           0.463104\n",
      "0.620000 2.121922 1.664499           0.457424\n",
      "0.630000 2.094486 1.643189           0.451297\n",
      "0.640000 2.064983 1.620253           0.444730\n",
      "0.650000 2.033442 1.595711           0.437731\n",
      "0.660000 1.999894 1.569588           0.430306\n",
      "0.670000 1.964373 1.541910           0.422463\n",
      "0.680000 1.926913 1.512702           0.414211\n",
      "0.690000 1.887551 1.481994           0.405557\n",
      "0.700000 1.846327 1.449815           0.396512\n",
      "0.710000 1.803280 1.416197           0.387083\n",
      "0.720000 1.758454 1.381173           0.377281\n",
      "0.730000 1.711892 1.344776           0.367117\n",
      "0.740000 1.663642 1.307043           0.356599\n",
      "0.750000 1.613749 1.268010           0.345739\n",
      "0.760000 1.562263 1.227715           0.334548\n",
      "0.770000 1.509236 1.186198           0.323038\n",
      "0.780000 1.454720 1.143500           0.311219\n",
      "0.790000 1.398767 1.099662           0.299105\n",
      "0.800000 1.341435 1.054728           0.286707\n",
      "0.810000 1.282778 1.008741           0.274038\n",
      "0.820000 1.222856 0.961746           0.261110\n",
      "0.830000 1.161727 0.913789           0.247937\n",
      "0.840000 1.099451 0.864919           0.234533\n",
      "0.850000 1.036090 0.815181           0.220909\n",
      "0.860000 0.971707 0.764627           0.207081\n",
      "0.870000 0.906365 0.713304           0.193061\n",
      "0.880000 0.840128 0.661264           0.178865\n",
      "0.890000 0.773063 0.608557           0.164505\n",
      "0.900000 0.705234 0.555236           0.149998\n",
      "0.910000 0.636709 0.501353           0.135357\n",
      "0.920000 0.567556 0.446960           0.120596\n",
      "0.930000 0.497843 0.392113           0.105731\n",
      "0.940000 0.427639 0.336863           0.090776\n",
      "0.950000 0.357012 0.281266           0.075746\n",
      "0.960000 0.286034 0.225377           0.060657\n",
      "0.970000 0.214773 0.169250           0.045522\n",
      "0.980000 0.143300 0.112942           0.030358\n",
      "0.990000 0.071685 0.056506           0.015179\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.55\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.074130 0.058250           0.015880\n",
      "0.020000 0.148186 0.116459           0.031727\n",
      "0.030000 0.222096 0.174568           0.047528\n",
      "0.040000 0.295787 0.232521           0.063266\n",
      "0.050000 0.369187 0.290260           0.078926\n",
      "0.060000 0.442221 0.347728           0.094493\n",
      "0.070000 0.514820 0.404869           0.109951\n",
      "0.080000 0.586910 0.461625           0.125286\n",
      "0.090000 0.658421 0.517940           0.140481\n",
      "0.100000 0.729283 0.573759           0.155524\n",
      "0.110000 0.799424 0.629026           0.170398\n",
      "0.120000 0.868777 0.683687           0.185090\n",
      "0.130000 0.937272 0.737688           0.199584\n",
      "0.140000 1.004843 0.790974           0.213868\n",
      "0.150000 1.071421 0.843494           0.227928\n",
      "0.160000 1.136943 0.895194           0.241748\n",
      "0.170000 1.201342 0.946025           0.255317\n",
      "0.180000 1.264556 0.995934           0.268622\n",
      "0.190000 1.326521 1.044873           0.281648\n",
      "0.200000 1.387178 1.092793           0.294385\n",
      "0.210000 1.446466 1.139647           0.306818\n",
      "0.220000 1.504326 1.185388           0.318938\n",
      "0.230000 1.560702 1.229970           0.330731\n",
      "0.240000 1.615537 1.273350           0.342187\n",
      "0.250000 1.668778 1.315483           0.353295\n",
      "0.260000 1.720372 1.356329           0.364044\n",
      "0.270000 1.770268 1.395845           0.374423\n",
      "0.280000 1.818418 1.433994           0.384424\n",
      "0.290000 1.864772 1.470737           0.394035\n",
      "0.300000 1.909287 1.506037           0.403250\n",
      "0.310000 1.951917 1.539860           0.412057\n",
      "0.320000 1.992621 1.572170           0.420451\n",
      "0.330000 2.031358 1.602937           0.428421\n",
      "0.340000 2.068091 1.632129           0.435962\n",
      "0.350000 2.102783 1.659717           0.443065\n",
      "0.360000 2.135399 1.685674           0.449725\n",
      "0.370000 2.165909 1.709973           0.455935\n",
      "0.380000 2.194280 1.732590           0.461690\n",
      "0.390000 2.220486 1.753503           0.466984\n",
      "0.400000 2.244501 1.772689           0.471812\n",
      "0.410000 2.266301 1.790131           0.476170\n",
      "0.420000 2.285864 1.805809           0.480055\n",
      "0.430000 2.303172 1.819709           0.483462\n",
      "0.440000 2.318206 1.831817           0.486390\n",
      "0.450000 2.330953 1.842119           0.488834\n",
      "0.460000 2.341399 1.850605           0.490794\n",
      "0.470000 2.349535 1.857266           0.492268\n",
      "0.480000 2.355351 1.862096           0.493256\n",
      "0.490000 2.358844 1.865089           0.493755\n",
      "0.500000 2.360008 1.866242           0.493767\n",
      "0.510000 2.358844 1.865552           0.493291\n",
      "0.520000 2.355351 1.863022           0.492330\n",
      "0.530000 2.349535 1.858651           0.490883\n",
      "0.540000 2.341399 1.852445           0.488954\n",
      "0.550000 2.330953 1.844409           0.486543\n",
      "0.560000 2.318206 1.834551           0.483655\n",
      "0.570000 2.303172 1.822879           0.480293\n",
      "0.580000 2.285864 1.809405           0.476459\n",
      "0.590000 2.266301 1.794142           0.472159\n",
      "0.600000 2.244501 1.777105           0.467397\n",
      "0.610000 2.220486 1.758309           0.462178\n",
      "0.620000 2.194280 1.737773           0.456507\n",
      "0.630000 2.165909 1.715517           0.450392\n",
      "0.640000 2.135399 1.691562           0.443837\n",
      "0.650000 2.102783 1.665932           0.436851\n",
      "0.660000 2.068091 1.638651           0.429440\n",
      "0.670000 2.031358 1.609746           0.421612\n",
      "0.680000 1.992621 1.579245           0.413376\n",
      "0.690000 1.951917 1.547178           0.404739\n",
      "0.700000 1.909287 1.513576           0.395711\n",
      "0.710000 1.864772 1.478472           0.386300\n",
      "0.720000 1.818418 1.441900           0.376518\n",
      "0.730000 1.770268 1.403896           0.366373\n",
      "0.740000 1.720372 1.364497           0.355875\n",
      "0.750000 1.668778 1.323741           0.345037\n",
      "0.760000 1.615537 1.281669           0.333868\n",
      "0.770000 1.560702 1.238321           0.322380\n",
      "0.780000 1.504326 1.193740           0.310586\n",
      "0.790000 1.446466 1.147971           0.298495\n",
      "0.800000 1.387178 1.101056           0.286122\n",
      "0.810000 1.326521 1.053043           0.273478\n",
      "0.820000 1.264556 1.003979           0.260576\n",
      "0.830000 1.201342 0.953912           0.247430\n",
      "0.840000 1.136943 0.902891           0.234052\n",
      "0.850000 1.071421 0.850966           0.220456\n",
      "0.860000 1.004843 0.798187           0.206655\n",
      "0.870000 0.937272 0.744608           0.192664\n",
      "0.880000 0.868777 0.690280           0.178497\n",
      "0.890000 0.799424 0.635258           0.164167\n",
      "0.900000 0.729283 0.579594           0.149689\n",
      "0.910000 0.658421 0.523344           0.135077\n",
      "0.920000 0.586910 0.466563           0.120347\n",
      "0.930000 0.514820 0.409308           0.105512\n",
      "0.940000 0.442221 0.351634           0.090588\n",
      "0.950000 0.369187 0.293597           0.075589\n",
      "0.960000 0.295787 0.235257           0.060531\n",
      "0.970000 0.222096 0.176669           0.045428\n",
      "0.980000 0.148186 0.117891           0.030295\n",
      "0.990000 0.074130 0.058982           0.015147\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.56\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.076647 0.060814           0.015833\n",
      "0.020000 0.153219 0.121584           0.031635\n",
      "0.030000 0.229639 0.182250           0.047390\n",
      "0.040000 0.305833 0.242751           0.063082\n",
      "0.050000 0.381725 0.303029           0.078696\n",
      "0.060000 0.457241 0.363023           0.094217\n",
      "0.070000 0.532305 0.422675           0.109630\n",
      "0.080000 0.606843 0.481924           0.124919\n",
      "0.090000 0.680783 0.540713           0.140070\n",
      "0.100000 0.754051 0.598983           0.155068\n",
      "0.110000 0.826575 0.656677           0.169898\n",
      "0.120000 0.898283 0.713736           0.184547\n",
      "0.130000 0.969105 0.770106           0.198998\n",
      "0.140000 1.038970 0.825730           0.213240\n",
      "0.150000 1.107810 0.880552           0.227257\n",
      "0.160000 1.175556 0.934519           0.241037\n",
      "0.170000 1.242143 0.987577           0.254566\n",
      "0.180000 1.307504 1.039673           0.267830\n",
      "0.190000 1.371574 1.090756           0.280818\n",
      "0.200000 1.434291 1.140775           0.293516\n",
      "0.210000 1.495592 1.189679           0.305912\n",
      "0.220000 1.555417 1.237422           0.317995\n",
      "0.230000 1.613707 1.283954           0.329753\n",
      "0.240000 1.670405 1.329231           0.341174\n",
      "0.250000 1.725454 1.373206           0.352248\n",
      "0.260000 1.778801 1.415836           0.362965\n",
      "0.270000 1.830392 1.457079           0.373312\n",
      "0.280000 1.880176 1.496894           0.383282\n",
      "0.290000 1.928105 1.535240           0.392865\n",
      "0.300000 1.974132 1.572081           0.402051\n",
      "0.310000 2.018210 1.607378           0.410832\n",
      "0.320000 2.060296 1.641097           0.419199\n",
      "0.330000 2.100349 1.673204           0.427145\n",
      "0.340000 2.138329 1.703667           0.434662\n",
      "0.350000 2.174199 1.732455           0.441744\n",
      "0.360000 2.207924 1.759541           0.448383\n",
      "0.370000 2.239469 1.784895           0.454574\n",
      "0.380000 2.268804 1.808494           0.460310\n",
      "0.390000 2.295900 1.830313           0.465587\n",
      "0.400000 2.320731 1.850331           0.470400\n",
      "0.410000 2.343271 1.868527           0.474744\n",
      "0.420000 2.363499 1.884883           0.478616\n",
      "0.430000 2.381394 1.899382           0.482012\n",
      "0.440000 2.396939 1.912009           0.484930\n",
      "0.450000 2.410118 1.922752           0.487366\n",
      "0.460000 2.420919 1.931600           0.489319\n",
      "0.470000 2.429331 1.938544           0.490788\n",
      "0.480000 2.435346 1.943575           0.491771\n",
      "0.490000 2.438957 1.946689           0.492268\n",
      "0.500000 2.440161 1.947882           0.492279\n",
      "0.510000 2.438957 1.947153           0.491804\n",
      "0.520000 2.435346 1.944502           0.490844\n",
      "0.530000 2.429331 1.939931           0.489401\n",
      "0.540000 2.420919 1.933443           0.487476\n",
      "0.550000 2.410118 1.925046           0.485072\n",
      "0.560000 2.396939 1.914747           0.482192\n",
      "0.570000 2.381394 1.902556           0.478838\n",
      "0.580000 2.363499 1.888484           0.475015\n",
      "0.590000 2.343271 1.872544           0.470727\n",
      "0.600000 2.320731 1.854753           0.465978\n",
      "0.610000 2.295900 1.835126           0.460774\n",
      "0.620000 2.268804 1.813684           0.455120\n",
      "0.630000 2.239469 1.790447           0.449022\n",
      "0.640000 2.207924 1.765437           0.442487\n",
      "0.650000 2.174199 1.738678           0.435521\n",
      "0.660000 2.138329 1.710197           0.428132\n",
      "0.670000 2.100349 1.680022           0.420327\n",
      "0.680000 2.060296 1.648181           0.412115\n",
      "0.690000 2.018210 1.614706           0.403503\n",
      "0.700000 1.974132 1.579630           0.394502\n",
      "0.710000 1.928105 1.542986           0.385119\n",
      "0.720000 1.880176 1.504810           0.375366\n",
      "0.730000 1.830392 1.465141           0.365251\n",
      "0.740000 1.778801 1.424015           0.354785\n",
      "0.750000 1.725454 1.381475           0.343979\n",
      "0.760000 1.670405 1.337561           0.332844\n",
      "0.770000 1.613707 1.292316           0.321391\n",
      "0.780000 1.555417 1.245785           0.309632\n",
      "0.790000 1.495592 1.198014           0.297578\n",
      "0.800000 1.434291 1.149049           0.285242\n",
      "0.810000 1.371574 1.098937           0.272636\n",
      "0.820000 1.307504 1.047730           0.259774\n",
      "0.830000 1.242143 0.995476           0.246667\n",
      "0.840000 1.175556 0.942226           0.233330\n",
      "0.850000 1.107810 0.888034           0.219775\n",
      "0.860000 1.038970 0.832953           0.206017\n",
      "0.870000 0.969105 0.777036           0.192069\n",
      "0.880000 0.898283 0.720338           0.177945\n",
      "0.890000 0.826575 0.662916           0.163659\n",
      "0.900000 0.754051 0.604826           0.149225\n",
      "0.910000 0.680783 0.546125           0.134659\n",
      "0.920000 0.606843 0.486870           0.119974\n",
      "0.930000 0.532305 0.427120           0.105185\n",
      "0.940000 0.457241 0.366934           0.090307\n",
      "0.950000 0.381725 0.306371           0.075354\n",
      "0.960000 0.305833 0.245491           0.060343\n",
      "0.970000 0.229639 0.184353           0.045286\n",
      "0.980000 0.153219 0.123018           0.030201\n",
      "0.990000 0.076647 0.061547           0.015100\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.5700000000000001\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.079241 0.063470           0.015771\n",
      "0.020000 0.158403 0.126893           0.031510\n",
      "0.030000 0.237409 0.190207           0.047202\n",
      "0.040000 0.316181 0.253349           0.062832\n",
      "0.050000 0.394641 0.316257           0.078384\n",
      "0.060000 0.472711 0.378868           0.093843\n",
      "0.070000 0.550315 0.441120           0.109194\n",
      "0.080000 0.627375 0.502953           0.124423\n",
      "0.090000 0.703817 0.564304           0.139513\n",
      "0.100000 0.779564 0.625113           0.154451\n",
      "0.110000 0.854542 0.685319           0.169222\n",
      "0.120000 0.928676 0.744864           0.183812\n",
      "0.130000 1.001894 0.803688           0.198205\n",
      "0.140000 1.074123 0.861733           0.212390\n",
      "0.150000 1.145292 0.918941           0.226351\n",
      "0.160000 1.215331 0.975256           0.240075\n",
      "0.170000 1.284170 1.030621           0.253549\n",
      "0.180000 1.351742 1.084982           0.266760\n",
      "0.190000 1.417980 1.138285           0.279695\n",
      "0.200000 1.482819 1.190477           0.292342\n",
      "0.210000 1.546194 1.241506           0.304688\n",
      "0.220000 1.608043 1.291321           0.316722\n",
      "0.230000 1.668306 1.339874           0.328432\n",
      "0.240000 1.726922 1.387115           0.339807\n",
      "0.250000 1.783834 1.432998           0.350836\n",
      "0.260000 1.838985 1.477477           0.361508\n",
      "0.270000 1.892322 1.520508           0.371814\n",
      "0.280000 1.943791 1.562048           0.381743\n",
      "0.290000 1.993341 1.602055           0.391286\n",
      "0.300000 2.040925 1.640490           0.400434\n",
      "0.310000 2.086494 1.677315           0.409179\n",
      "0.320000 2.130004 1.712493           0.417512\n",
      "0.330000 2.171413 1.745988           0.425425\n",
      "0.340000 2.210678 1.777767           0.432911\n",
      "0.350000 2.247762 1.807799           0.439963\n",
      "0.360000 2.282627 1.836052           0.446574\n",
      "0.370000 2.315240 1.862500           0.452739\n",
      "0.380000 2.345567 1.887116           0.458451\n",
      "0.390000 2.373580 1.909874           0.463706\n",
      "0.400000 2.399251 1.930752           0.468499\n",
      "0.410000 2.422554 1.949729           0.472824\n",
      "0.420000 2.443466 1.966786           0.476680\n",
      "0.430000 2.461967 1.981905           0.480061\n",
      "0.440000 2.478037 1.995072           0.482966\n",
      "0.450000 2.491663 2.006272           0.485391\n",
      "0.460000 2.502829 2.015494           0.487336\n",
      "0.470000 2.511526 2.022729           0.488797\n",
      "0.480000 2.517744 2.027968           0.489775\n",
      "0.490000 2.521477 2.031208           0.490269\n",
      "0.500000 2.522722 2.032443           0.490279\n",
      "0.510000 2.521477 2.031672           0.489805\n",
      "0.520000 2.517744 2.028896           0.488848\n",
      "0.530000 2.511526 2.024116           0.487410\n",
      "0.540000 2.502829 2.017337           0.485492\n",
      "0.550000 2.491663 2.008566           0.483097\n",
      "0.560000 2.478037 1.997810           0.480227\n",
      "0.570000 2.461967 1.985080           0.476886\n",
      "0.580000 2.443466 1.970388           0.473078\n",
      "0.590000 2.422554 1.953748           0.468806\n",
      "0.600000 2.399251 1.935175           0.464076\n",
      "0.610000 2.373580 1.914688           0.458892\n",
      "0.620000 2.345567 1.892307           0.453260\n",
      "0.630000 2.315240 1.868053           0.447186\n",
      "0.640000 2.282627 1.841950           0.440677\n",
      "0.650000 2.247762 1.814023           0.433739\n",
      "0.660000 2.210678 1.784299           0.426379\n",
      "0.670000 2.171413 1.752808           0.418605\n",
      "0.680000 2.130004 1.719579           0.410426\n",
      "0.690000 2.086494 1.684645           0.401849\n",
      "0.700000 2.040925 1.648041           0.392883\n",
      "0.710000 1.993341 1.609803           0.383539\n",
      "0.720000 1.943791 1.569966           0.373824\n",
      "0.730000 1.892322 1.528571           0.363750\n",
      "0.740000 1.838985 1.485658           0.353327\n",
      "0.750000 1.783834 1.441269           0.342565\n",
      "0.760000 1.726922 1.395447           0.331474\n",
      "0.770000 1.668306 1.348238           0.320068\n",
      "0.780000 1.608043 1.299687           0.308356\n",
      "0.790000 1.546194 1.249842           0.296352\n",
      "0.800000 1.482819 1.198753           0.284066\n",
      "0.810000 1.417980 1.146468           0.271512\n",
      "0.820000 1.351742 1.093040           0.258702\n",
      "0.830000 1.284170 1.038521           0.245649\n",
      "0.840000 1.215331 0.982964           0.232366\n",
      "0.850000 1.145292 0.926425           0.218867\n",
      "0.860000 1.074123 0.868958           0.205165\n",
      "0.870000 1.001894 0.810619           0.191274\n",
      "0.880000 0.928676 0.751468           0.177208\n",
      "0.890000 0.854542 0.691561           0.162981\n",
      "0.900000 0.779564 0.630957           0.148607\n",
      "0.910000 0.703817 0.569717           0.134100\n",
      "0.920000 0.627375 0.507899           0.119476\n",
      "0.930000 0.550315 0.445566           0.104748\n",
      "0.940000 0.472711 0.382779           0.089932\n",
      "0.950000 0.394641 0.319599           0.075041\n",
      "0.960000 0.316181 0.256089           0.060092\n",
      "0.970000 0.237409 0.192311           0.045098\n",
      "0.980000 0.158403 0.128328           0.030075\n",
      "0.990000 0.079241 0.064203           0.015037\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.58\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.081912 0.066221           0.015691\n",
      "0.020000 0.163743 0.132392           0.031351\n",
      "0.030000 0.245413 0.198448           0.046965\n",
      "0.040000 0.326841 0.264325           0.062516\n",
      "0.050000 0.407946 0.329956           0.077989\n",
      "0.060000 0.488648 0.395277           0.093371\n",
      "0.070000 0.568868 0.460223           0.108645\n",
      "0.080000 0.648527 0.524731           0.123796\n",
      "0.090000 0.727545 0.588735           0.138810\n",
      "0.100000 0.805846 0.652174           0.153672\n",
      "0.110000 0.883352 0.714983           0.168368\n",
      "0.120000 0.959985 0.777101           0.182884\n",
      "0.130000 1.035671 0.838467           0.197205\n",
      "0.140000 1.110336 0.899019           0.211317\n",
      "0.150000 1.183904 0.958697           0.225207\n",
      "0.160000 1.256304 1.017443           0.238861\n",
      "0.170000 1.327464 1.075198           0.252267\n",
      "0.180000 1.397315 1.131904           0.265410\n",
      "0.190000 1.465786 1.187506           0.278279\n",
      "0.200000 1.532810 1.241949           0.290861\n",
      "0.210000 1.598322 1.295178           0.303145\n",
      "0.220000 1.662257 1.347140           0.315117\n",
      "0.230000 1.724551 1.397784           0.326767\n",
      "0.240000 1.785143 1.447060           0.338083\n",
      "0.250000 1.843974 1.494918           0.349056\n",
      "0.260000 1.900985 1.541312           0.359673\n",
      "0.270000 1.956119 1.586194           0.369926\n",
      "0.280000 2.009324 1.629520           0.379804\n",
      "0.290000 2.060545 1.671247           0.389297\n",
      "0.300000 2.109733 1.711334           0.398398\n",
      "0.310000 2.156838 1.749741           0.407098\n",
      "0.320000 2.201815 1.786428           0.415387\n",
      "0.330000 2.244620 1.821360           0.423259\n",
      "0.340000 2.285209 1.854502           0.430706\n",
      "0.350000 2.323543 1.885821           0.437722\n",
      "0.360000 2.359583 1.915285           0.444298\n",
      "0.370000 2.393296 1.942865           0.450431\n",
      "0.380000 2.424646 1.968533           0.456113\n",
      "0.390000 2.453603 1.992263           0.461340\n",
      "0.400000 2.480139 2.014032           0.466107\n",
      "0.410000 2.504228 2.033818           0.470410\n",
      "0.420000 2.525845 2.051600           0.474244\n",
      "0.430000 2.544969 2.067362           0.477608\n",
      "0.440000 2.561582 2.081086           0.480496\n",
      "0.450000 2.575667 2.092758           0.482908\n",
      "0.460000 2.587210 2.102368           0.484842\n",
      "0.470000 2.596199 2.109904           0.486295\n",
      "0.480000 2.602627 2.115360           0.487267\n",
      "0.490000 2.606486 2.118728           0.487758\n",
      "0.500000 2.607773 2.120006           0.487766\n",
      "0.510000 2.606486 2.119192           0.487294\n",
      "0.520000 2.602627 2.116286           0.486341\n",
      "0.530000 2.596199 2.111290           0.484909\n",
      "0.540000 2.587210 2.104210           0.483000\n",
      "0.550000 2.575667 2.095051           0.480616\n",
      "0.560000 2.561582 2.083822           0.477760\n",
      "0.570000 2.544969 2.070534           0.474436\n",
      "0.580000 2.525845 2.055199           0.470646\n",
      "0.590000 2.504228 2.037833           0.466395\n",
      "0.600000 2.480139 2.018451           0.461688\n",
      "0.610000 2.453603 1.997073           0.456530\n",
      "0.620000 2.424646 1.973719           0.450927\n",
      "0.630000 2.393296 1.948413           0.444883\n",
      "0.640000 2.359583 1.921177           0.438406\n",
      "0.650000 2.323543 1.892040           0.431503\n",
      "0.660000 2.285209 1.861029           0.424180\n",
      "0.670000 2.244620 1.828174           0.416446\n",
      "0.680000 2.201815 1.793508           0.408307\n",
      "0.690000 2.156838 1.757064           0.399774\n",
      "0.700000 2.109733 1.718878           0.390854\n",
      "0.710000 2.060545 1.678988           0.381557\n",
      "0.720000 2.009324 1.637431           0.371892\n",
      "0.730000 1.956119 1.594250           0.361869\n",
      "0.740000 1.900985 1.549485           0.351499\n",
      "0.750000 1.843974 1.503182           0.340792\n",
      "0.760000 1.785143 1.455385           0.329758\n",
      "0.770000 1.724551 1.406141           0.318410\n",
      "0.780000 1.662257 1.355498           0.306759\n",
      "0.790000 1.598322 1.303507           0.294816\n",
      "0.800000 1.532810 1.250217           0.282593\n",
      "0.810000 1.465786 1.195682           0.270103\n",
      "0.820000 1.397315 1.139955           0.257359\n",
      "0.830000 1.327464 1.083091           0.244374\n",
      "0.840000 1.256304 1.025145           0.231159\n",
      "0.850000 1.183904 0.966174           0.217730\n",
      "0.860000 1.110336 0.906237           0.204099\n",
      "0.870000 1.035671 0.845392           0.190280\n",
      "0.880000 0.959985 0.783699           0.176286\n",
      "0.890000 0.883352 0.721219           0.162133\n",
      "0.900000 0.805846 0.658013           0.147833\n",
      "0.910000 0.727545 0.594143           0.133402\n",
      "0.920000 0.648527 0.529673           0.118854\n",
      "0.930000 0.568868 0.464666           0.104202\n",
      "0.940000 0.488648 0.399185           0.089463\n",
      "0.950000 0.407946 0.333296           0.074650\n",
      "0.960000 0.326841 0.267062           0.059778\n",
      "0.970000 0.245413 0.200550           0.044863\n",
      "0.980000 0.163743 0.133826           0.029918\n",
      "0.990000 0.081912 0.066953           0.014959\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.59\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.084664 0.069069           0.015596\n",
      "0.020000 0.169245 0.138085           0.031160\n",
      "0.030000 0.253659 0.206982           0.046678\n",
      "0.040000 0.337823 0.275689           0.062134\n",
      "0.050000 0.421653 0.344140           0.077513\n",
      "0.060000 0.505067 0.412267           0.092800\n",
      "0.070000 0.587983 0.480003           0.107980\n",
      "0.080000 0.670318 0.547280           0.123038\n",
      "0.090000 0.751992 0.614032           0.137960\n",
      "0.100000 0.832924 0.680192           0.152731\n",
      "0.110000 0.913033 0.745696           0.167337\n",
      "0.120000 0.992242 0.810479           0.181763\n",
      "0.130000 1.070472 0.874476           0.195996\n",
      "0.140000 1.147645 0.937623           0.210021\n",
      "0.150000 1.223685 0.999859           0.223826\n",
      "0.160000 1.298518 1.061122           0.237396\n",
      "0.170000 1.372069 1.121351           0.250718\n",
      "0.180000 1.444266 1.180486           0.263781\n",
      "0.190000 1.515038 1.238468           0.276570\n",
      "0.200000 1.584315 1.295241           0.289074\n",
      "0.210000 1.652028 1.350747           0.301281\n",
      "0.220000 1.718111 1.404932           0.313179\n",
      "0.230000 1.782499 1.457742           0.324757\n",
      "0.240000 1.845127 1.509124           0.336003\n",
      "0.250000 1.905934 1.559027           0.346907\n",
      "0.260000 1.964860 1.607402           0.357459\n",
      "0.270000 2.021848 1.654201           0.367647\n",
      "0.280000 2.076840 1.699376           0.377464\n",
      "0.290000 2.129782 1.742884           0.386898\n",
      "0.300000 2.180623 1.784680           0.395942\n",
      "0.310000 2.229311 1.824724           0.404587\n",
      "0.320000 2.275800 1.862975           0.412825\n",
      "0.330000 2.320042 1.899395           0.420647\n",
      "0.340000 2.361995 1.933948           0.428048\n",
      "0.350000 2.401617 1.966598           0.435019\n",
      "0.360000 2.438869 1.997315           0.441554\n",
      "0.370000 2.473714 2.026066           0.447648\n",
      "0.380000 2.506118 2.052824           0.453294\n",
      "0.390000 2.536048 2.077560           0.458488\n",
      "0.400000 2.563476 2.100252           0.463224\n",
      "0.410000 2.588374 2.120874           0.467499\n",
      "0.420000 2.610717 2.139408           0.471309\n",
      "0.430000 2.630484 2.155833           0.474651\n",
      "0.440000 2.647655 2.170134           0.477521\n",
      "0.450000 2.662213 2.182296           0.479917\n",
      "0.460000 2.674144 2.192307           0.481837\n",
      "0.470000 2.683436 2.200155           0.483281\n",
      "0.480000 2.690079 2.205833           0.484246\n",
      "0.490000 2.694068 2.209336           0.484732\n",
      "0.500000 2.695398 2.210658           0.484740\n",
      "0.510000 2.694068 2.209799           0.484269\n",
      "0.520000 2.690079 2.206758           0.483321\n",
      "0.530000 2.683436 2.201538           0.481897\n",
      "0.540000 2.674144 2.194145           0.479999\n",
      "0.550000 2.662213 2.184584           0.477629\n",
      "0.560000 2.647655 2.172865           0.474790\n",
      "0.570000 2.630484 2.158999           0.471485\n",
      "0.580000 2.610717 2.142999           0.467718\n",
      "0.590000 2.588374 2.124881           0.463493\n",
      "0.600000 2.563476 2.104661           0.458814\n",
      "0.610000 2.536048 2.082360           0.453688\n",
      "0.620000 2.506118 2.058000           0.448118\n",
      "0.630000 2.473714 2.031603           0.442111\n",
      "0.640000 2.438869 2.003195           0.435674\n",
      "0.650000 2.401617 1.972805           0.428812\n",
      "0.660000 2.361995 1.940461           0.421535\n",
      "0.670000 2.320042 1.906195           0.413848\n",
      "0.680000 2.275800 1.870040           0.405759\n",
      "0.690000 2.229311 1.832033           0.397278\n",
      "0.700000 2.180623 1.792209           0.388413\n",
      "0.710000 2.129782 1.750609           0.379174\n",
      "0.720000 2.076840 1.707271           0.369568\n",
      "0.730000 2.021848 1.662240           0.359608\n",
      "0.740000 1.964860 1.615559           0.349301\n",
      "0.750000 1.905934 1.567274           0.338660\n",
      "0.760000 1.845127 1.517431           0.327695\n",
      "0.770000 1.782499 1.466081           0.316417\n",
      "0.780000 1.718111 1.413273           0.304838\n",
      "0.790000 1.652028 1.359059           0.292969\n",
      "0.800000 1.584315 1.303492           0.280823\n",
      "0.810000 1.515038 1.246628           0.268411\n",
      "0.820000 1.444266 1.188520           0.255746\n",
      "0.830000 1.372069 1.129228           0.242841\n",
      "0.840000 1.298518 1.068808           0.229710\n",
      "0.850000 1.223685 1.007321           0.216364\n",
      "0.860000 1.147645 0.944827           0.202818\n",
      "0.870000 1.070472 0.881386           0.189085\n",
      "0.880000 0.992242 0.817063           0.175179\n",
      "0.890000 0.913033 0.751919           0.161114\n",
      "0.900000 0.832924 0.686019           0.146904\n",
      "0.910000 0.751992 0.619429           0.132563\n",
      "0.920000 0.670318 0.552212           0.118106\n",
      "0.930000 0.587983 0.484436           0.103547\n",
      "0.940000 0.505067 0.416167           0.088900\n",
      "0.950000 0.421653 0.347473           0.074180\n",
      "0.960000 0.337823 0.278421           0.059402\n",
      "0.970000 0.253659 0.209079           0.044580\n",
      "0.980000 0.169245 0.139516           0.029729\n",
      "0.990000 0.084664 0.069800           0.014864\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.6\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.087500 0.072017           0.015483\n",
      "0.020000 0.174915 0.143979           0.030935\n",
      "0.030000 0.262156 0.215815           0.046341\n",
      "0.040000 0.349139 0.287453           0.061686\n",
      "0.050000 0.435777 0.358823           0.076954\n",
      "0.060000 0.521985 0.429855           0.092130\n",
      "0.070000 0.607678 0.500478           0.107200\n",
      "0.080000 0.692771 0.570621           0.122150\n",
      "0.090000 0.777181 0.640217           0.136964\n",
      "0.100000 0.860823 0.709196           0.151628\n",
      "0.110000 0.943617 0.777489           0.166128\n",
      "0.120000 1.025478 0.845029           0.180449\n",
      "0.130000 1.106328 0.911750           0.194579\n",
      "0.140000 1.186086 0.977584           0.208502\n",
      "0.150000 1.264674 1.042468           0.222206\n",
      "0.160000 1.342013 1.106336           0.235678\n",
      "0.170000 1.418028 1.169125           0.248903\n",
      "0.180000 1.492644 1.230773           0.261870\n",
      "0.190000 1.565786 1.291220           0.274567\n",
      "0.200000 1.637384 1.350404           0.286980\n",
      "0.210000 1.707365 1.408267           0.299098\n",
      "0.220000 1.775661 1.464752           0.310909\n",
      "0.230000 1.842205 1.519803           0.322402\n",
      "0.240000 1.906931 1.573365           0.333566\n",
      "0.250000 1.969776 1.625385           0.344390\n",
      "0.260000 2.030676 1.675811           0.354864\n",
      "0.270000 2.089572 1.724594           0.364978\n",
      "0.280000 2.146406 1.771683           0.374723\n",
      "0.290000 2.201122 1.817034           0.384088\n",
      "0.300000 2.253665 1.860600           0.393066\n",
      "0.310000 2.303985 1.902338           0.401647\n",
      "0.320000 2.352030 1.942206           0.409824\n",
      "0.330000 2.397755 1.980166           0.417589\n",
      "0.340000 2.441113 2.016179           0.424934\n",
      "0.350000 2.482062 2.050208           0.431854\n",
      "0.360000 2.520562 2.082221           0.438341\n",
      "0.370000 2.556574 2.112185           0.444389\n",
      "0.380000 2.590063 2.140070           0.449993\n",
      "0.390000 2.620996 2.165848           0.455148\n",
      "0.400000 2.649342 2.189493           0.459849\n",
      "0.410000 2.675074 2.210982           0.464093\n",
      "0.420000 2.698166 2.230292           0.467874\n",
      "0.430000 2.718595 2.247405           0.471190\n",
      "0.440000 2.736341 2.262303           0.474038\n",
      "0.450000 2.751387 2.274971           0.476416\n",
      "0.460000 2.763717 2.285396           0.478321\n",
      "0.470000 2.773320 2.293567           0.479753\n",
      "0.480000 2.780186 2.299476           0.480710\n",
      "0.490000 2.784309 2.303117           0.481192\n",
      "0.500000 2.785683 2.304484           0.481199\n",
      "0.510000 2.784309 2.303578           0.480731\n",
      "0.520000 2.780186 2.300398           0.479789\n",
      "0.530000 2.773320 2.294946           0.478374\n",
      "0.540000 2.763717 2.287228           0.476489\n",
      "0.550000 2.751387 2.277251           0.474136\n",
      "0.560000 2.736341 2.265025           0.471316\n",
      "0.570000 2.718595 2.250560           0.468035\n",
      "0.580000 2.698166 2.233872           0.464294\n",
      "0.590000 2.675074 2.214975           0.460099\n",
      "0.600000 2.649342 2.193888           0.455454\n",
      "0.610000 2.620996 2.170632           0.450364\n",
      "0.620000 2.590063 2.145229           0.444834\n",
      "0.630000 2.556574 2.117703           0.438870\n",
      "0.640000 2.520562 2.088082           0.432479\n",
      "0.650000 2.482062 2.056394           0.425668\n",
      "0.660000 2.441113 2.022671           0.418442\n",
      "0.670000 2.397755 1.986944           0.410811\n",
      "0.680000 2.352030 1.949249           0.402781\n",
      "0.690000 2.303985 1.909623           0.394362\n",
      "0.700000 2.253665 1.868104           0.385561\n",
      "0.710000 2.201122 1.824733           0.376388\n",
      "0.720000 2.146406 1.779553           0.366853\n",
      "0.730000 2.089572 1.732607           0.356965\n",
      "0.740000 2.030676 1.683942           0.346734\n",
      "0.750000 1.969776 1.633605           0.336170\n",
      "0.760000 1.906931 1.581646           0.325285\n",
      "0.770000 1.842205 1.528116           0.314090\n",
      "0.780000 1.775661 1.473067           0.302595\n",
      "0.790000 1.707365 1.416552           0.290813\n",
      "0.800000 1.637384 1.358629           0.278755\n",
      "0.810000 1.565786 1.299352           0.266434\n",
      "0.820000 1.492644 1.238782           0.253862\n",
      "0.830000 1.418028 1.176976           0.241052\n",
      "0.840000 1.342013 1.113997           0.228016\n",
      "0.850000 1.264674 1.049905           0.214769\n",
      "0.860000 1.186086 0.984764           0.201322\n",
      "0.870000 1.106328 0.918638           0.187690\n",
      "0.880000 1.025478 0.851592           0.173887\n",
      "0.890000 0.943617 0.783691           0.159925\n",
      "0.900000 0.860823 0.715004           0.145820\n",
      "0.910000 0.777181 0.645596           0.131585\n",
      "0.920000 0.692771 0.575537           0.117234\n",
      "0.930000 0.607678 0.504896           0.102782\n",
      "0.940000 0.521985 0.433742           0.088243\n",
      "0.950000 0.435777 0.362145           0.073632\n",
      "0.960000 0.349139 0.290176           0.058963\n",
      "0.970000 0.262156 0.217906           0.044250\n",
      "0.980000 0.174915 0.145405           0.029509\n",
      "0.990000 0.087500 0.072746           0.014754\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.61\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.090423 0.075068           0.015354\n",
      "0.020000 0.180756 0.150079           0.030678\n",
      "0.030000 0.270911 0.224956           0.045955\n",
      "0.040000 0.360799 0.299628           0.061171\n",
      "0.050000 0.450331 0.374019           0.076312\n",
      "0.060000 0.539418 0.448056           0.091362\n",
      "0.070000 0.627973 0.521667           0.106306\n",
      "0.080000 0.715908 0.594777           0.121131\n",
      "0.090000 0.803137 0.667316           0.135821\n",
      "0.100000 0.889573 0.739211           0.150362\n",
      "0.110000 0.975131 0.810390           0.164741\n",
      "0.120000 1.059727 0.880785           0.178942\n",
      "0.130000 1.143277 0.950324           0.192953\n",
      "0.140000 1.225699 1.018939           0.206760\n",
      "0.150000 1.306911 1.086562           0.220349\n",
      "0.160000 1.386833 1.153126           0.233707\n",
      "0.170000 1.465387 1.218565           0.246822\n",
      "0.180000 1.542494 1.282814           0.259680\n",
      "0.190000 1.618080 1.345810           0.272270\n",
      "0.200000 1.692068 1.407490           0.284578\n",
      "0.210000 1.764387 1.467792           0.296594\n",
      "0.220000 1.834964 1.526658           0.308306\n",
      "0.230000 1.903731 1.584028           0.319702\n",
      "0.240000 1.970618 1.639846           0.330772\n",
      "0.250000 2.035561 1.694056           0.341505\n",
      "0.260000 2.098495 1.746605           0.351891\n",
      "0.270000 2.159359 1.797439           0.361919\n",
      "0.280000 2.218091 1.846510           0.371581\n",
      "0.290000 2.274634 1.893767           0.380867\n",
      "0.300000 2.328932 1.939163           0.389769\n",
      "0.310000 2.380932 1.982655           0.398277\n",
      "0.320000 2.430582 2.024198           0.406385\n",
      "0.330000 2.477834 2.063750           0.414084\n",
      "0.340000 2.522640 2.101273           0.421367\n",
      "0.350000 2.564957 2.136730           0.428227\n",
      "0.360000 2.604742 2.170083           0.434659\n",
      "0.370000 2.641957 2.201302           0.440656\n",
      "0.380000 2.676565 2.230353           0.446212\n",
      "0.390000 2.708531 2.257208           0.451323\n",
      "0.400000 2.737824 2.281840           0.455983\n",
      "0.410000 2.764415 2.304225           0.460190\n",
      "0.420000 2.788278 2.324340           0.463939\n",
      "0.430000 2.809390 2.342164           0.467226\n",
      "0.440000 2.827728 2.357679           0.470049\n",
      "0.450000 2.843277 2.370871           0.472406\n",
      "0.460000 2.856019 2.381724           0.474295\n",
      "0.470000 2.865943 2.390229           0.475713\n",
      "0.480000 2.873038 2.396376           0.476661\n",
      "0.490000 2.877298 2.400159           0.477138\n",
      "0.500000 2.878718 2.401574           0.477144\n",
      "0.510000 2.877298 2.400619           0.476679\n",
      "0.520000 2.873038 2.397294           0.475744\n",
      "0.530000 2.865943 2.391602           0.474341\n",
      "0.540000 2.856019 2.383548           0.472470\n",
      "0.550000 2.843277 2.373141           0.470136\n",
      "0.560000 2.827728 2.360389           0.467339\n",
      "0.570000 2.809390 2.345305           0.464085\n",
      "0.580000 2.788278 2.327903           0.460375\n",
      "0.590000 2.764415 2.308201           0.456214\n",
      "0.600000 2.737824 2.286216           0.451607\n",
      "0.610000 2.708531 2.261971           0.446559\n",
      "0.620000 2.676565 2.235489           0.441075\n",
      "0.630000 2.641957 2.206796           0.435161\n",
      "0.640000 2.604742 2.175919           0.428824\n",
      "0.650000 2.564957 2.142888           0.422069\n",
      "0.660000 2.522640 2.107737           0.414904\n",
      "0.670000 2.477834 2.070498           0.407336\n",
      "0.680000 2.430582 2.031209           0.399373\n",
      "0.690000 2.380932 1.989908           0.391024\n",
      "0.700000 2.328932 1.946635           0.382297\n",
      "0.710000 2.274634 1.901432           0.373202\n",
      "0.720000 2.218091 1.854344           0.363746\n",
      "0.730000 2.159359 1.805418           0.353941\n",
      "0.740000 2.098495 1.754699           0.343796\n",
      "0.750000 2.035561 1.702240           0.333321\n",
      "0.760000 1.970618 1.648090           0.322528\n",
      "0.770000 1.903731 1.592304           0.311427\n",
      "0.780000 1.834964 1.534935           0.300029\n",
      "0.790000 1.764387 1.476041           0.288346\n",
      "0.800000 1.692068 1.415678           0.276390\n",
      "0.810000 1.618080 1.353907           0.264173\n",
      "0.820000 1.542494 1.290787           0.251707\n",
      "0.830000 1.465387 1.226381           0.239005\n",
      "0.840000 1.386833 1.160753           0.226080\n",
      "0.850000 1.306911 1.093966           0.212945\n",
      "0.860000 1.225699 1.026087           0.199612\n",
      "0.870000 1.143277 0.957182           0.186095\n",
      "0.880000 1.059727 0.887318           0.172409\n",
      "0.890000 0.975131 0.816566           0.158566\n",
      "0.900000 0.889573 0.744993           0.144580\n",
      "0.910000 0.803137 0.672671           0.130465\n",
      "0.920000 0.715908 0.599672           0.116236\n",
      "0.930000 0.627973 0.526066           0.101907\n",
      "0.940000 0.539418 0.451926           0.087492\n",
      "0.950000 0.450331 0.377326           0.073005\n",
      "0.960000 0.360799 0.302338           0.058461\n",
      "0.970000 0.270911 0.227038           0.043873\n",
      "0.980000 0.180756 0.151498           0.029258\n",
      "0.990000 0.090423 0.075794           0.014629\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.62\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.093434 0.078225           0.015209\n",
      "0.020000 0.186776 0.156389           0.030387\n",
      "0.030000 0.279934 0.234415           0.045519\n",
      "0.040000 0.372816 0.312224           0.060591\n",
      "0.050000 0.465329 0.389741           0.075588\n",
      "0.060000 0.557384 0.466888           0.090495\n",
      "0.070000 0.648888 0.543590           0.105298\n",
      "0.080000 0.739752 0.619771           0.119981\n",
      "0.090000 0.829886 0.695354           0.134531\n",
      "0.100000 0.919200 0.770266           0.148934\n",
      "0.110000 1.007608 0.844432           0.163176\n",
      "0.120000 1.095021 0.917779           0.177242\n",
      "0.130000 1.181354 0.990234           0.191120\n",
      "0.140000 1.266521 1.061726           0.204795\n",
      "0.150000 1.350438 1.132183           0.218255\n",
      "0.160000 1.433022 1.201537           0.231485\n",
      "0.170000 1.514192 1.269717           0.244475\n",
      "0.180000 1.593868 1.336657           0.257210\n",
      "0.190000 1.671970 1.402291           0.269680\n",
      "0.200000 1.748423 1.466552           0.281871\n",
      "0.210000 1.823150 1.529379           0.293772\n",
      "0.220000 1.896078 1.590707           0.305371\n",
      "0.230000 1.967135 1.650476           0.316658\n",
      "0.240000 2.036250 1.708628           0.327622\n",
      "0.250000 2.103356 1.765104           0.338252\n",
      "0.260000 2.168386 1.819848           0.348538\n",
      "0.270000 2.231277 1.872806           0.358471\n",
      "0.280000 2.291965 1.923925           0.368040\n",
      "0.290000 2.350391 1.973155           0.377237\n",
      "0.300000 2.406498 2.020445           0.386052\n",
      "0.310000 2.460230 2.065751           0.394479\n",
      "0.320000 2.511534 2.109025           0.402508\n",
      "0.330000 2.560359 2.150226           0.410133\n",
      "0.340000 2.606657 2.189311           0.417346\n",
      "0.350000 2.650383 2.226243           0.424140\n",
      "0.360000 2.691494 2.260984           0.430510\n",
      "0.370000 2.729948 2.293500           0.436448\n",
      "0.380000 2.765708 2.323758           0.441951\n",
      "0.390000 2.798739 2.351727           0.447012\n",
      "0.400000 2.829008 2.377381           0.451627\n",
      "0.410000 2.856485 2.400692           0.455793\n",
      "0.420000 2.881143 2.421638           0.459504\n",
      "0.430000 2.902957 2.440198           0.462759\n",
      "0.440000 2.921907 2.456352           0.465555\n",
      "0.450000 2.937973 2.470084           0.467888\n",
      "0.460000 2.951139 2.481382           0.469758\n",
      "0.470000 2.961394 2.490231           0.471162\n",
      "0.480000 2.968725 2.496625           0.472100\n",
      "0.490000 2.973127 2.500555           0.472572\n",
      "0.500000 2.974595 2.502018           0.472577\n",
      "0.510000 2.973127 2.501012           0.472115\n",
      "0.520000 2.968725 2.497537           0.471188\n",
      "0.530000 2.961394 2.491596           0.469797\n",
      "0.540000 2.951139 2.483195           0.467944\n",
      "0.550000 2.937973 2.472342           0.465631\n",
      "0.560000 2.921907 2.459046           0.462860\n",
      "0.570000 2.902957 2.443321           0.459636\n",
      "0.580000 2.881143 2.425182           0.455961\n",
      "0.590000 2.856485 2.404645           0.451839\n",
      "0.600000 2.829008 2.381732           0.447276\n",
      "0.610000 2.798739 2.356464           0.442275\n",
      "0.620000 2.765708 2.328865           0.436843\n",
      "0.630000 2.729948 2.298963           0.430985\n",
      "0.640000 2.691494 2.266787           0.424707\n",
      "0.650000 2.650383 2.232367           0.418016\n",
      "0.660000 2.606657 2.195738           0.410919\n",
      "0.670000 2.560359 2.156935           0.403423\n",
      "0.680000 2.511534 2.115997           0.395537\n",
      "0.690000 2.460230 2.072962           0.387267\n",
      "0.700000 2.406498 2.027874           0.378623\n",
      "0.710000 2.350391 1.980777           0.369614\n",
      "0.720000 2.291965 1.931716           0.360249\n",
      "0.730000 2.231277 1.880739           0.350537\n",
      "0.740000 2.168386 1.827897           0.340489\n",
      "0.750000 2.103356 1.773241           0.330115\n",
      "0.760000 2.036250 1.716826           0.319425\n",
      "0.770000 1.967135 1.658705           0.308430\n",
      "0.780000 1.896078 1.598937           0.297141\n",
      "0.790000 1.823150 1.537580           0.285570\n",
      "0.800000 1.748423 1.474694           0.273729\n",
      "0.810000 1.671970 1.410342           0.261629\n",
      "0.820000 1.593868 1.344585           0.249283\n",
      "0.830000 1.514192 1.277489           0.236703\n",
      "0.840000 1.433022 1.209121           0.223901\n",
      "0.850000 1.350438 1.139546           0.210892\n",
      "0.860000 1.266521 1.068833           0.197687\n",
      "0.870000 1.181354 0.997053           0.184301\n",
      "0.880000 1.095021 0.924276           0.170746\n",
      "0.890000 1.007608 0.850572           0.157036\n",
      "0.900000 0.919200 0.776016           0.143185\n",
      "0.910000 0.829886 0.700679           0.129206\n",
      "0.920000 0.739752 0.624637           0.115115\n",
      "0.930000 0.648888 0.547964           0.100923\n",
      "0.940000 0.557384 0.470736           0.086647\n",
      "0.950000 0.465329 0.393029           0.072300\n",
      "0.960000 0.372816 0.314920           0.057896\n",
      "0.970000 0.279934 0.236485           0.043450\n",
      "0.980000 0.186776 0.157801           0.028975\n",
      "0.990000 0.093434 0.078947           0.014487\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.63\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.096538 0.081491           0.015047\n",
      "0.020000 0.192981 0.162918           0.030063\n",
      "0.030000 0.289233 0.244199           0.045034\n",
      "0.040000 0.385200 0.325255           0.059946\n",
      "0.050000 0.480787 0.406005           0.074782\n",
      "0.060000 0.575899 0.486369           0.089530\n",
      "0.070000 0.670443 0.566269           0.104175\n",
      "0.080000 0.764325 0.645624           0.118701\n",
      "0.090000 0.857453 0.724357           0.133096\n",
      "0.100000 0.949735 0.802390           0.147345\n",
      "0.110000 1.041080 0.879645           0.161435\n",
      "0.120000 1.131397 0.956046           0.175350\n",
      "0.130000 1.220597 1.031518           0.189079\n",
      "0.140000 1.308593 1.105985           0.202608\n",
      "0.150000 1.395298 1.179374           0.215923\n",
      "0.160000 1.480625 1.251613           0.229013\n",
      "0.170000 1.564492 1.322629           0.241863\n",
      "0.180000 1.646814 1.392352           0.254462\n",
      "0.190000 1.727511 1.460714           0.266797\n",
      "0.200000 1.806504 1.527646           0.278857\n",
      "0.210000 1.883713 1.593082           0.290631\n",
      "0.220000 1.959064 1.656958           0.302106\n",
      "0.230000 2.032481 1.719209           0.313271\n",
      "0.240000 2.103892 1.779775           0.324117\n",
      "0.250000 2.173227 1.838594           0.334633\n",
      "0.260000 2.240418 1.895609           0.344808\n",
      "0.270000 2.305397 1.950763           0.354634\n",
      "0.280000 2.368101 2.004002           0.364100\n",
      "0.290000 2.428468 2.055271           0.373197\n",
      "0.300000 2.486439 2.104521           0.381918\n",
      "0.310000 2.541956 2.151702           0.390254\n",
      "0.320000 2.594964 2.196767           0.398196\n",
      "0.330000 2.645411 2.239672           0.405739\n",
      "0.340000 2.693247 2.280374           0.412873\n",
      "0.350000 2.738426 2.318832           0.419594\n",
      "0.360000 2.780902 2.355008           0.425894\n",
      "0.370000 2.820634 2.388866           0.431768\n",
      "0.380000 2.857582 2.420371           0.437211\n",
      "0.390000 2.891710 2.449493           0.442217\n",
      "0.400000 2.922984 2.476202           0.446782\n",
      "0.410000 2.951374 2.500472           0.450902\n",
      "0.420000 2.976851 2.522278           0.454573\n",
      "0.430000 2.999390 2.541598           0.457792\n",
      "0.440000 3.018969 2.558412           0.460557\n",
      "0.450000 3.035569 2.572704           0.462864\n",
      "0.460000 3.049173 2.584460           0.464713\n",
      "0.470000 3.059768 2.593666           0.466101\n",
      "0.480000 3.067343 2.600314           0.467029\n",
      "0.490000 3.071891 2.604397           0.467494\n",
      "0.500000 3.073407 2.605910           0.467498\n",
      "0.510000 3.071891 2.604850           0.467040\n",
      "0.520000 3.067343 2.601220           0.466123\n",
      "0.530000 3.059768 2.595022           0.464746\n",
      "0.540000 3.049173 2.586261           0.462912\n",
      "0.550000 3.035569 2.574946           0.460622\n",
      "0.560000 3.018969 2.561088           0.457881\n",
      "0.570000 2.999390 2.544700           0.454690\n",
      "0.580000 2.976851 2.525797           0.451054\n",
      "0.590000 2.951374 2.504398           0.446976\n",
      "0.600000 2.922984 2.480523           0.442461\n",
      "0.610000 2.891710 2.454197           0.437513\n",
      "0.620000 2.857582 2.425443           0.432139\n",
      "0.630000 2.820634 2.394291           0.426343\n",
      "0.640000 2.780902 2.360770           0.420132\n",
      "0.650000 2.738426 2.324914           0.413512\n",
      "0.660000 2.693247 2.286756           0.406491\n",
      "0.670000 2.645411 2.246336           0.399075\n",
      "0.680000 2.594964 2.203691           0.391273\n",
      "0.690000 2.541956 2.158864           0.383092\n",
      "0.700000 2.486439 2.111898           0.374540\n",
      "0.710000 2.428468 2.062840           0.365628\n",
      "0.720000 2.368101 2.011738           0.356363\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.730000 2.305397 1.958641           0.346755\n",
      "0.740000 2.240418 1.903603           0.336815\n",
      "0.750000 2.173227 1.846675           0.326552\n",
      "0.760000 2.103892 1.787916           0.315976\n",
      "0.770000 2.032481 1.727381           0.305100\n",
      "0.780000 1.959064 1.665131           0.293932\n",
      "0.790000 1.883713 1.601227           0.282486\n",
      "0.800000 1.806504 1.535732           0.270772\n",
      "0.810000 1.727511 1.468709           0.258802\n",
      "0.820000 1.646814 1.400225           0.246589\n",
      "0.830000 1.564492 1.330347           0.234144\n",
      "0.840000 1.480625 1.259144           0.221481\n",
      "0.850000 1.395298 1.186686           0.208612\n",
      "0.860000 1.308593 1.113044           0.195550\n",
      "0.870000 1.220597 1.038290           0.182308\n",
      "0.880000 1.131397 0.962498           0.168899\n",
      "0.890000 1.041080 0.885743           0.155337\n",
      "0.900000 0.949735 0.808100           0.141635\n",
      "0.910000 0.857453 0.729645           0.127808\n",
      "0.920000 0.764325 0.650457           0.113868\n",
      "0.930000 0.670443 0.570612           0.099831\n",
      "0.940000 0.575899 0.490190           0.085709\n",
      "0.950000 0.480787 0.409270           0.071517\n",
      "0.960000 0.385200 0.327931           0.057269\n",
      "0.970000 0.289233 0.246254           0.042979\n",
      "0.980000 0.192981 0.164320           0.028661\n",
      "0.990000 0.096538 0.082208           0.014330\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.64\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.099737 0.084869           0.014868\n",
      "0.020000 0.199376 0.169669           0.029707\n",
      "0.030000 0.298818 0.254318           0.044500\n",
      "0.040000 0.397965 0.338731           0.059234\n",
      "0.050000 0.496719 0.422824           0.073895\n",
      "0.060000 0.594983 0.506516           0.088467\n",
      "0.070000 0.692660 0.589722           0.102938\n",
      "0.080000 0.789653 0.672361           0.117292\n",
      "0.090000 0.885867 0.754352           0.131516\n",
      "0.100000 0.981207 0.835612           0.145595\n",
      "0.110000 1.075579 0.916062           0.159517\n",
      "0.120000 1.168889 0.995622           0.173267\n",
      "0.130000 1.261045 1.074213           0.186833\n",
      "0.140000 1.351957 1.151757           0.200200\n",
      "0.150000 1.441535 1.228178           0.213357\n",
      "0.160000 1.529690 1.303400           0.226290\n",
      "0.170000 1.616336 1.377349           0.238987\n",
      "0.180000 1.701386 1.449950           0.251436\n",
      "0.190000 1.784757 1.521133           0.263624\n",
      "0.200000 1.866367 1.590827           0.275540\n",
      "0.210000 1.946135 1.658963           0.287173\n",
      "0.220000 2.023983 1.725472           0.298511\n",
      "0.230000 2.099833 1.790290           0.309543\n",
      "0.240000 2.173611 1.853351           0.320259\n",
      "0.250000 2.245243 1.914594           0.330649\n",
      "0.260000 2.314660 1.973958           0.340703\n",
      "0.270000 2.381793 2.031383           0.350410\n",
      "0.280000 2.446575 2.086812           0.359763\n",
      "0.290000 2.508942 2.140191           0.368751\n",
      "0.300000 2.568834 2.191467           0.377368\n",
      "0.310000 2.626191 2.240587           0.385603\n",
      "0.320000 2.680955 2.287505           0.393450\n",
      "0.330000 2.733074 2.332172           0.400902\n",
      "0.340000 2.782496 2.374545           0.407951\n",
      "0.350000 2.829172 2.414581           0.414591\n",
      "0.360000 2.873055 2.452240           0.420815\n",
      "0.370000 2.914104 2.487485           0.426618\n",
      "0.380000 2.952276 2.520281           0.431995\n",
      "0.390000 2.987535 2.550594           0.436941\n",
      "0.400000 3.019846 2.578395           0.441450\n",
      "0.410000 3.049176 2.603656           0.445520\n",
      "0.420000 3.075497 2.626350           0.449147\n",
      "0.430000 3.098783 2.646456           0.452327\n",
      "0.440000 3.119011 2.663954           0.455057\n",
      "0.450000 3.136161 2.678824           0.457337\n",
      "0.460000 3.150216 2.691053           0.459162\n",
      "0.470000 3.161162 2.700628           0.460533\n",
      "0.480000 3.168988 2.707539           0.461449\n",
      "0.490000 3.173687 2.711779           0.461908\n",
      "0.500000 3.175254 2.713343           0.461911\n",
      "0.510000 3.173687 2.712229           0.461458\n",
      "0.520000 3.168988 2.708438           0.460550\n",
      "0.530000 3.161162 2.701973           0.459189\n",
      "0.540000 3.150216 2.692840           0.457376\n",
      "0.550000 3.136161 2.681048           0.455113\n",
      "0.560000 3.119011 2.666607           0.452404\n",
      "0.570000 3.098783 2.649533           0.449250\n",
      "0.580000 3.075497 2.629840           0.445657\n",
      "0.590000 3.049176 2.607549           0.441627\n",
      "0.600000 3.019846 2.582681           0.437165\n",
      "0.610000 2.987535 2.555259           0.432276\n",
      "0.620000 2.952276 2.525311           0.426965\n",
      "0.630000 2.914104 2.492866           0.421238\n",
      "0.640000 2.873055 2.457955           0.415100\n",
      "0.650000 2.829172 2.420613           0.408559\n",
      "0.660000 2.782496 2.380875           0.401621\n",
      "0.670000 2.733074 2.338781           0.394293\n",
      "0.680000 2.680955 2.294372           0.386584\n",
      "0.690000 2.626191 2.247691           0.378500\n",
      "0.700000 2.568834 2.198784           0.370051\n",
      "0.710000 2.508942 2.147698           0.361244\n",
      "0.720000 2.446575 2.094485           0.352090\n",
      "0.730000 2.381793 2.039196           0.342597\n",
      "0.740000 2.314660 1.981885           0.332775\n",
      "0.750000 2.245243 1.922609           0.322634\n",
      "0.760000 2.173611 1.861425           0.312185\n",
      "0.770000 2.099833 1.798395           0.301438\n",
      "0.780000 2.023983 1.733578           0.290404\n",
      "0.790000 1.946135 1.667041           0.279095\n",
      "0.800000 1.866367 1.598846           0.267521\n",
      "0.810000 1.784757 1.529063           0.255694\n",
      "0.820000 1.701386 1.457759           0.243627\n",
      "0.830000 1.616336 1.385004           0.231332\n",
      "0.840000 1.529690 1.310870           0.218820\n",
      "0.850000 1.441535 1.235430           0.206105\n",
      "0.860000 1.351957 1.158757           0.193200\n",
      "0.870000 1.261045 1.080929           0.180116\n",
      "0.880000 1.168889 1.002020           0.166869\n",
      "0.890000 1.075579 0.922109           0.153469\n",
      "0.900000 0.981207 0.841275           0.139932\n",
      "0.910000 0.885867 0.759597           0.126271\n",
      "0.920000 0.789653 0.677155           0.112499\n",
      "0.930000 0.692660 0.594030           0.098630\n",
      "0.940000 0.594983 0.510306           0.084678\n",
      "0.950000 0.496719 0.426063           0.070656\n",
      "0.960000 0.397965 0.341385           0.056579\n",
      "0.970000 0.298818 0.256356           0.042461\n",
      "0.980000 0.199376 0.171060           0.028316\n",
      "0.990000 0.099737 0.085579           0.014158\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.65\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.103035 0.088361           0.014674\n",
      "0.020000 0.205968 0.176650           0.029317\n",
      "0.030000 0.308697 0.264780           0.043917\n",
      "0.040000 0.411122 0.352664           0.058458\n",
      "0.050000 0.513142 0.440215           0.072926\n",
      "0.060000 0.614655 0.527347           0.087308\n",
      "0.070000 0.715561 0.613973           0.101588\n",
      "0.080000 0.815761 0.700007           0.115754\n",
      "0.090000 0.915156 0.785365           0.129791\n",
      "0.100000 1.013648 0.869963           0.143685\n",
      "0.110000 1.111140 0.953715           0.157424\n",
      "0.120000 1.207535 1.036541           0.170994\n",
      "0.130000 1.302738 1.118357           0.184381\n",
      "0.140000 1.396656 1.199083           0.197573\n",
      "0.150000 1.489195 1.278639           0.210556\n",
      "0.160000 1.580265 1.356946           0.223319\n",
      "0.170000 1.669775 1.433926           0.235849\n",
      "0.180000 1.757637 1.509504           0.248134\n",
      "0.190000 1.843765 1.583604           0.260161\n",
      "0.200000 1.928073 1.656152           0.271921\n",
      "0.210000 2.010478 1.727079           0.283400\n",
      "0.220000 2.090900 1.796311           0.294588\n",
      "0.230000 2.169257 1.863782           0.305475\n",
      "0.240000 2.245475 1.929425           0.316050\n",
      "0.250000 2.319476 1.993173           0.326302\n",
      "0.260000 2.391187 2.054964           0.336223\n",
      "0.270000 2.460540 2.114737           0.345803\n",
      "0.280000 2.527464 2.172432           0.355032\n",
      "0.290000 2.591893 2.227992           0.363901\n",
      "0.300000 2.653765 2.281361           0.372403\n",
      "0.310000 2.713018 2.332488           0.380530\n",
      "0.320000 2.769593 2.381320           0.388273\n",
      "0.330000 2.823435 2.427809           0.395626\n",
      "0.340000 2.874491 2.471909           0.402582\n",
      "0.350000 2.922710 2.513577           0.409133\n",
      "0.360000 2.968044 2.552769           0.415275\n",
      "0.370000 3.010450 2.589449           0.421001\n",
      "0.380000 3.049884 2.623578           0.426306\n",
      "0.390000 3.086309 2.655123           0.431186\n",
      "0.400000 3.119688 2.684052           0.435635\n",
      "0.410000 3.149988 2.710337           0.439651\n",
      "0.420000 3.177179 2.733950           0.443229\n",
      "0.430000 3.201235 2.754869           0.446366\n",
      "0.440000 3.222132 2.773072           0.449060\n",
      "0.450000 3.239849 2.788540           0.451308\n",
      "0.460000 3.254368 2.801259           0.453109\n",
      "0.470000 3.265676 2.811215           0.454461\n",
      "0.480000 3.273761 2.818398           0.455363\n",
      "0.490000 3.278615 2.822799           0.455816\n",
      "0.500000 3.280234 2.824416           0.455818\n",
      "0.510000 3.278615 2.823245           0.455370\n",
      "0.520000 3.273761 2.819287           0.454474\n",
      "0.530000 3.265676 2.812546           0.453129\n",
      "0.540000 3.254368 2.803029           0.451340\n",
      "0.550000 3.239849 2.790743           0.449106\n",
      "0.560000 3.222132 2.775700           0.446431\n",
      "0.570000 3.201235 2.757916           0.443319\n",
      "0.580000 3.177179 2.737407           0.439772\n",
      "0.590000 3.149988 2.714193           0.435794\n",
      "0.600000 3.119688 2.688297           0.431391\n",
      "0.610000 3.086309 2.659744           0.426565\n",
      "0.620000 3.049884 2.628560           0.421324\n",
      "0.630000 3.010450 2.594778           0.415671\n",
      "0.640000 2.968044 2.558430           0.409614\n",
      "0.650000 2.922710 2.519551           0.403159\n",
      "0.660000 2.874491 2.478179           0.396312\n",
      "0.670000 2.823435 2.434354           0.389081\n",
      "0.680000 2.769593 2.388121           0.381472\n",
      "0.690000 2.713018 2.339523           0.373495\n",
      "0.700000 2.653765 2.288609           0.365156\n",
      "0.710000 2.591893 2.235428           0.356466\n",
      "0.720000 2.527464 2.180032           0.347432\n",
      "0.730000 2.460540 2.122476           0.338064\n",
      "0.740000 2.391187 2.062816           0.328371\n",
      "0.750000 2.319476 2.001111           0.318364\n",
      "0.760000 2.245475 1.937422           0.308053\n",
      "0.770000 2.169257 1.871810           0.297448\n",
      "0.780000 2.090900 1.804340           0.286559\n",
      "0.790000 2.010478 1.735079           0.275399\n",
      "0.800000 1.928073 1.664095           0.263978\n",
      "0.810000 1.843765 1.591457           0.252308\n",
      "0.820000 1.757637 1.517237           0.240400\n",
      "0.830000 1.669775 1.441508           0.228267\n",
      "0.840000 1.580265 1.364344           0.215921\n",
      "0.850000 1.489195 1.285821           0.203374\n",
      "0.860000 1.396656 1.206017           0.190639\n",
      "0.870000 1.302738 1.125009           0.177729\n",
      "0.880000 1.207535 1.042878           0.164656\n",
      "0.890000 1.111140 0.959705           0.151434\n",
      "0.900000 1.013648 0.875571           0.138077\n",
      "0.910000 0.915156 0.790560           0.124596\n",
      "0.920000 0.815761 0.704754           0.111006\n",
      "0.930000 0.715561 0.618240           0.097321\n",
      "0.940000 0.614655 0.531101           0.083554\n",
      "0.950000 0.513142 0.443423           0.069719\n",
      "0.960000 0.411122 0.355294           0.055829\n",
      "0.970000 0.308697 0.266799           0.041898\n",
      "0.980000 0.205968 0.178027           0.027940\n",
      "0.990000 0.103035 0.089065           0.013970\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.66\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.106434 0.091971           0.014463\n",
      "0.020000 0.212763 0.183867           0.028896\n",
      "0.030000 0.318881 0.275596           0.043285\n",
      "0.040000 0.424686 0.367069           0.057617\n",
      "0.050000 0.530071 0.458194           0.071877\n",
      "0.060000 0.634933 0.548881           0.086051\n",
      "0.070000 0.739168 0.639042           0.100126\n",
      "0.080000 0.842674 0.728586           0.114088\n",
      "0.090000 0.945348 0.817425           0.127923\n",
      "0.100000 1.047089 0.905472           0.141617\n",
      "0.110000 1.147797 0.992639           0.155158\n",
      "0.120000 1.247372 1.078841           0.168531\n",
      "0.130000 1.345716 1.163991           0.181725\n",
      "0.140000 1.442733 1.248006           0.194727\n",
      "0.150000 1.538325 1.330802           0.207523\n",
      "0.160000 1.632399 1.412297           0.220102\n",
      "0.170000 1.724862 1.492412           0.232451\n",
      "0.180000 1.815623 1.571065           0.244558\n",
      "0.190000 1.904592 1.648181           0.256412\n",
      "0.200000 1.991682 1.723681           0.268001\n",
      "0.210000 2.076806 1.797492           0.279314\n",
      "0.220000 2.159880 1.869539           0.290341\n",
      "0.230000 2.240823 1.939753           0.301070\n",
      "0.240000 2.319555 2.008063           0.311492\n",
      "0.250000 2.395997 2.074401           0.321596\n",
      "0.260000 2.470075 2.138702           0.331373\n",
      "0.270000 2.541715 2.200901           0.340814\n",
      "0.280000 2.610847 2.260938           0.349909\n",
      "0.290000 2.677402 2.318752           0.358650\n",
      "0.300000 2.741315 2.374286           0.367029\n",
      "0.310000 2.802523 2.427485           0.375037\n",
      "0.320000 2.860964 2.478296           0.382668\n",
      "0.330000 2.916583 2.526668           0.389914\n",
      "0.340000 2.969323 2.572554           0.396769\n",
      "0.350000 3.019133 2.615908           0.403225\n",
      "0.360000 3.065963 2.656686           0.409277\n",
      "0.370000 3.109767 2.694847           0.414920\n",
      "0.380000 3.150503 2.730355           0.420148\n",
      "0.390000 3.188129 2.763173           0.424956\n",
      "0.400000 3.222609 2.793269           0.429341\n",
      "0.410000 3.253909 2.820612           0.433297\n",
      "0.420000 3.281997 2.845175           0.436823\n",
      "0.430000 3.306847 2.866933           0.439914\n",
      "0.440000 3.328433 2.885865           0.442568\n",
      "0.450000 3.346734 2.901951           0.444783\n",
      "0.460000 3.361733 2.915176           0.446557\n",
      "0.470000 3.373414 2.925525           0.447889\n",
      "0.480000 3.381765 2.932988           0.448777\n",
      "0.490000 3.386780 2.937558           0.449222\n",
      "0.500000 3.388452 2.939228           0.449223\n",
      "0.510000 3.386780 2.937998           0.448781\n",
      "0.520000 3.381765 2.933868           0.447897\n",
      "0.530000 3.373414 2.926842           0.446572\n",
      "0.540000 3.361733 2.916926           0.444807\n",
      "0.550000 3.346734 2.904129           0.442605\n",
      "0.560000 3.328433 2.888465           0.439968\n",
      "0.570000 3.306847 2.869947           0.436900\n",
      "0.580000 3.281997 2.848594           0.433403\n",
      "0.590000 3.253909 2.824426           0.429483\n",
      "0.600000 3.222609 2.797467           0.425142\n",
      "0.610000 3.188129 2.767743           0.420386\n",
      "0.620000 3.150503 2.735283           0.415220\n",
      "0.630000 3.109767 2.700119           0.409648\n",
      "0.640000 3.065963 2.662284           0.403679\n",
      "0.650000 3.019133 2.621817           0.397316\n",
      "0.660000 2.969323 2.578755           0.390568\n",
      "0.670000 2.916583 2.533143           0.383440\n",
      "0.680000 2.860964 2.485023           0.375941\n",
      "0.690000 2.802523 2.434444           0.368079\n",
      "0.700000 2.741315 2.381454           0.359861\n",
      "0.710000 2.677402 2.326107           0.351296\n",
      "0.720000 2.610847 2.268455           0.342392\n",
      "0.730000 2.541715 2.208556           0.333159\n",
      "0.740000 2.470075 2.146468           0.323607\n",
      "0.750000 2.395997 2.082253           0.313745\n",
      "0.760000 2.319555 2.015973           0.303582\n",
      "0.770000 2.240823 1.947693           0.293130\n",
      "0.780000 2.159880 1.877481           0.282400\n",
      "0.790000 2.076806 1.805405           0.271401\n",
      "0.800000 1.991682 1.731537           0.260145\n",
      "0.810000 1.904592 1.655949           0.248644\n",
      "0.820000 1.815623 1.578715           0.236909\n",
      "0.830000 1.724862 1.499911           0.224951\n",
      "0.840000 1.632399 1.419615           0.212784\n",
      "0.850000 1.538325 1.337906           0.200419\n",
      "0.860000 1.442733 1.254864           0.187869\n",
      "0.870000 1.345716 1.170570           0.175146\n",
      "0.880000 1.247372 1.085109           0.162263\n",
      "0.890000 1.147797 0.998564           0.149233\n",
      "0.900000 1.047089 0.911020           0.136069\n",
      "0.910000 0.945348 0.822563           0.122785\n",
      "0.920000 0.842674 0.733281           0.109392\n",
      "0.930000 0.739168 0.643262           0.095906\n",
      "0.940000 0.634933 0.552594           0.082339\n",
      "0.950000 0.530071 0.461366           0.068704\n",
      "0.960000 0.424686 0.369669           0.055016\n",
      "0.970000 0.318881 0.277593           0.041288\n",
      "0.980000 0.212763 0.185229           0.027534\n",
      "0.990000 0.106434 0.092667           0.013766\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.67\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.109938 0.095703           0.014236\n",
      "0.020000 0.219768 0.191326           0.028442\n",
      "0.030000 0.329380 0.286775           0.042606\n",
      "0.040000 0.438668 0.381956           0.056712\n",
      "0.050000 0.547523 0.476775           0.070748\n",
      "0.060000 0.655837 0.571138           0.084700\n",
      "0.070000 0.763504 0.664951           0.098553\n",
      "0.080000 0.870418 0.758123           0.112295\n",
      "0.090000 0.976473 0.850560           0.125912\n",
      "0.100000 1.081564 0.942173           0.139391\n",
      "0.110000 1.185588 1.032869           0.152719\n",
      "0.120000 1.288441 1.122559           0.165882\n",
      "0.130000 1.390023 1.211155           0.178869\n",
      "0.140000 1.490234 1.298568           0.191665\n",
      "0.150000 1.588973 1.384713           0.204260\n",
      "0.160000 1.686145 1.469504           0.216640\n",
      "0.170000 1.781652 1.552858           0.228795\n",
      "0.180000 1.875401 1.634690           0.240711\n",
      "0.190000 1.967300 1.714922           0.252378\n",
      "0.200000 2.057257 1.793472           0.263784\n",
      "0.210000 2.145183 1.870264           0.274919\n",
      "0.220000 2.230993 1.945221           0.285772\n",
      "0.230000 2.314601 2.018269           0.296332\n",
      "0.240000 2.395925 2.089336           0.306589\n",
      "0.250000 2.474884 2.158350           0.316533\n",
      "0.260000 2.551401 2.225245           0.326156\n",
      "0.270000 2.625399 2.289952           0.335447\n",
      "0.280000 2.696807 2.352409           0.344399\n",
      "0.290000 2.765554 2.412552           0.353001\n",
      "0.300000 2.831571 2.470323           0.361248\n",
      "0.310000 2.894794 2.525664           0.369129\n",
      "0.320000 2.955160 2.578520           0.376639\n",
      "0.330000 3.012609 2.628839           0.383771\n",
      "0.340000 3.067086 2.676570           0.390516\n",
      "0.350000 3.118535 2.721666           0.396870\n",
      "0.360000 3.166908 2.764081           0.402826\n",
      "0.370000 3.212154 2.803775           0.408379\n",
      "0.380000 3.254231 2.840707           0.413524\n",
      "0.390000 3.293096 2.874840           0.418256\n",
      "0.400000 3.328711 2.906141           0.422570\n",
      "0.410000 3.361042 2.934578           0.426464\n",
      "0.420000 3.390055 2.960122           0.429933\n",
      "0.430000 3.415723 2.982748           0.432975\n",
      "0.440000 3.438019 3.002433           0.435586\n",
      "0.450000 3.456923 3.019158           0.437765\n",
      "0.460000 3.472416 3.032905           0.439511\n",
      "0.470000 3.484481 3.043660           0.440821\n",
      "0.480000 3.493108 3.051413           0.441694\n",
      "0.490000 3.498287 3.056156           0.442131\n",
      "0.500000 3.500014 3.057882           0.442132\n",
      "0.510000 3.498287 3.056591           0.441696\n",
      "0.520000 3.493108 3.052283           0.440825\n",
      "0.530000 3.484481 3.044961           0.439520\n",
      "0.540000 3.472416 3.034633           0.437782\n",
      "0.550000 3.456923 3.021309           0.435614\n",
      "0.560000 3.438019 3.005001           0.433018\n",
      "0.570000 3.415723 2.985725           0.429998\n",
      "0.580000 3.390055 2.963499           0.426556\n",
      "0.590000 3.361042 2.938345           0.422696\n",
      "0.600000 3.328711 2.910288           0.418423\n",
      "0.610000 3.293096 2.879354           0.413742\n",
      "0.620000 3.254231 2.845574           0.408656\n",
      "0.630000 3.212154 2.808981           0.403173\n",
      "0.640000 3.166908 2.769611           0.397296\n",
      "0.650000 3.118535 2.727502           0.391034\n",
      "0.660000 3.067086 2.682694           0.384391\n",
      "0.670000 3.012609 2.635233           0.377376\n",
      "0.680000 2.955160 2.585164           0.369995\n",
      "0.690000 2.894794 2.532537           0.362256\n",
      "0.700000 2.831571 2.477403           0.354168\n",
      "0.710000 2.765554 2.419816           0.345737\n",
      "0.720000 2.696807 2.359833           0.336974\n",
      "0.730000 2.625399 2.297512           0.327887\n",
      "0.740000 2.551401 2.232915           0.318485\n",
      "0.750000 2.474884 2.166105           0.308778\n",
      "0.760000 2.395925 2.097148           0.298776\n",
      "0.770000 2.314601 2.026111           0.288490\n",
      "0.780000 2.230993 1.953065           0.277928\n",
      "0.790000 2.145183 1.878080           0.267103\n",
      "0.800000 2.057257 1.801232           0.256025\n",
      "0.810000 1.967300 1.722594           0.244706\n",
      "0.820000 1.875401 1.642246           0.233156\n",
      "0.830000 1.781652 1.560264           0.221388\n",
      "0.840000 1.686145 1.476732           0.209413\n",
      "0.850000 1.588973 1.391730           0.197244\n",
      "0.860000 1.490234 1.305342           0.184892\n",
      "0.870000 1.390023 1.217653           0.172370\n",
      "0.880000 1.288441 1.128750           0.159691\n",
      "0.890000 1.185588 1.038720           0.146868\n",
      "0.900000 1.081564 0.947652           0.133912\n",
      "0.910000 0.976473 0.855635           0.120838\n",
      "0.920000 0.870418 0.762760           0.107658\n",
      "0.930000 0.763504 0.669120           0.094385\n",
      "0.940000 0.655837 0.574804           0.081033\n",
      "0.950000 0.547523 0.479908           0.067615\n",
      "0.960000 0.438668 0.384525           0.054144\n",
      "0.970000 0.329380 0.288747           0.040633\n",
      "0.980000 0.219768 0.192671           0.027097\n",
      "0.990000 0.109938 0.096390           0.013548\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.68\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.113551 0.099558           0.013993\n",
      "0.020000 0.226990 0.199033           0.027957\n",
      "0.030000 0.340205 0.298326           0.041878\n",
      "0.040000 0.453084 0.397340           0.055744\n",
      "0.050000 0.565515 0.495975           0.069540\n",
      "0.060000 0.677389 0.594136           0.083253\n",
      "0.070000 0.788595 0.691724           0.096870\n",
      "0.080000 0.899022 0.788644           0.110377\n",
      "0.090000 1.008562 0.884800           0.123762\n",
      "0.100000 1.117106 0.980096           0.137010\n",
      "0.110000 1.224548 1.074438           0.150110\n",
      "0.120000 1.330782 1.167734           0.163048\n",
      "0.130000 1.435702 1.259890           0.175812\n",
      "0.140000 1.539205 1.350816           0.188390\n",
      "0.150000 1.641190 1.440421           0.200769\n",
      "0.160000 1.741555 1.528617           0.212937\n",
      "0.170000 1.840201 1.615317           0.224883\n",
      "0.180000 1.937031 1.700435           0.236595\n",
      "0.190000 2.031949 1.783886           0.248063\n",
      "0.200000 2.124862 1.865589           0.259273\n",
      "0.210000 2.215678 1.945461           0.270217\n",
      "0.220000 2.304308 2.023424           0.280884\n",
      "0.230000 2.390663 2.099400           0.291263\n",
      "0.240000 2.474659 2.173315           0.301344\n",
      "0.250000 2.556213 2.245095           0.311118\n",
      "0.260000 2.635244 2.314669           0.320575\n",
      "0.270000 2.711675 2.381968           0.329707\n",
      "0.280000 2.785430 2.446925           0.338504\n",
      "0.290000 2.856435 2.509476           0.346959\n",
      "0.300000 2.924622 2.569558           0.355064\n",
      "0.310000 2.989922 2.627112           0.362810\n",
      "0.320000 3.052272 2.682081           0.370191\n",
      "0.330000 3.111609 2.734410           0.377199\n",
      "0.340000 3.167876 2.784047           0.383829\n",
      "0.350000 3.221017 2.830943           0.390073\n",
      "0.360000 3.270978 2.875052           0.395927\n",
      "0.370000 3.317712 2.916328           0.401384\n",
      "0.380000 3.361171 2.954731           0.406440\n",
      "0.390000 3.401313 2.990224           0.411090\n",
      "0.400000 3.438099 3.022769           0.415330\n",
      "0.410000 3.471492 3.052336           0.419156\n",
      "0.420000 3.501458 3.078894           0.422565\n",
      "0.430000 3.527970 3.102416           0.425554\n",
      "0.440000 3.550999 3.122880           0.428120\n",
      "0.450000 3.570524 3.140263           0.430261\n",
      "0.460000 3.586526 3.154550           0.431975\n",
      "0.470000 3.598988 3.165726           0.433262\n",
      "0.480000 3.607898 3.173778           0.434120\n",
      "0.490000 3.613248 3.178698           0.434549\n",
      "0.500000 3.615031 3.180482           0.434549\n",
      "0.510000 3.613248 3.179128           0.434120\n",
      "0.520000 3.607898 3.174635           0.433263\n",
      "0.530000 3.598988 3.167008           0.431979\n",
      "0.540000 3.586526 3.156255           0.430271\n",
      "0.550000 3.570524 3.142385           0.428139\n",
      "0.560000 3.550999 3.125412           0.425587\n",
      "0.570000 3.527970 3.105352           0.422618\n",
      "0.580000 3.501458 3.082224           0.419234\n",
      "0.590000 3.471492 3.056051           0.415440\n",
      "0.600000 3.438099 3.026859           0.411240\n",
      "0.610000 3.401313 2.994675           0.406638\n",
      "0.620000 3.361171 2.959532           0.401639\n",
      "0.630000 3.317712 2.921463           0.396249\n",
      "0.640000 3.270978 2.880505           0.390473\n",
      "0.650000 3.221017 2.836699           0.384317\n",
      "0.660000 3.167876 2.790088           0.377788\n",
      "0.670000 3.111609 2.740716           0.370893\n",
      "0.680000 3.052272 2.688634           0.363638\n",
      "0.690000 2.989922 2.633890           0.356032\n",
      "0.700000 2.924622 2.576540           0.348082\n",
      "0.710000 2.856435 2.516640           0.339796\n",
      "0.720000 2.785430 2.454247           0.331182\n",
      "0.730000 2.711675 2.389424           0.322251\n",
      "0.740000 2.635244 2.322234           0.313010\n",
      "0.750000 2.556213 2.252743           0.303470\n",
      "0.760000 2.474659 2.181020           0.293639\n",
      "0.770000 2.390663 2.107134           0.283529\n",
      "0.780000 2.304308 2.031159           0.273148\n",
      "0.790000 2.215678 1.953169           0.262509\n",
      "0.800000 2.124862 1.873241           0.251621\n",
      "0.810000 2.031949 1.791453           0.240496\n",
      "0.820000 1.937031 1.707886           0.229145\n",
      "0.830000 1.840201 1.622622           0.217578\n",
      "0.840000 1.741555 1.535745           0.205809\n",
      "0.850000 1.641190 1.447341           0.193849\n",
      "0.860000 1.539205 1.357496           0.181710\n",
      "0.870000 1.435702 1.266299           0.169403\n",
      "0.880000 1.330782 1.173840           0.156942\n",
      "0.890000 1.224548 1.080209           0.144339\n",
      "0.900000 1.117106 0.985500           0.131606\n",
      "0.910000 1.008562 0.889805           0.118757\n",
      "0.920000 0.899022 0.793218           0.105804\n",
      "0.930000 0.788595 0.695835           0.092759\n",
      "0.940000 0.677389 0.597752           0.079637\n",
      "0.950000 0.565515 0.499066           0.066450\n",
      "0.960000 0.453084 0.399873           0.053211\n",
      "0.970000 0.340205 0.300271           0.039933\n",
      "0.980000 0.226990 0.200360           0.026630\n",
      "0.990000 0.113551 0.100236           0.013314\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.6900000000000001\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.117276 0.103542           0.013734\n",
      "0.020000 0.234436 0.206996           0.027440\n",
      "0.030000 0.351364 0.310260           0.041104\n",
      "0.040000 0.467946 0.413233           0.054713\n",
      "0.050000 0.584066 0.515812           0.068254\n",
      "0.060000 0.699610 0.617896           0.081714\n",
      "0.070000 0.814463 0.719385           0.095079\n",
      "0.080000 0.928513 0.820177           0.108336\n",
      "0.090000 1.041646 0.920174           0.121472\n",
      "0.100000 1.153751 1.019276           0.134475\n",
      "0.110000 1.264718 1.117385           0.147332\n",
      "0.120000 1.374436 1.214405           0.160031\n",
      "0.130000 1.482798 1.310240           0.172558\n",
      "0.140000 1.589697 1.404794           0.184903\n",
      "0.150000 1.695026 1.497974           0.197052\n",
      "0.160000 1.798684 1.589688           0.208995\n",
      "0.170000 1.900566 1.679846           0.220720\n",
      "0.180000 2.000572 1.768357           0.232215\n",
      "0.190000 2.098604 1.855135           0.243469\n",
      "0.200000 2.194565 1.940093           0.254472\n",
      "0.210000 2.288360 2.023147           0.265213\n",
      "0.220000 2.379897 2.104215           0.275681\n",
      "0.230000 2.469085 2.183218           0.285867\n",
      "0.240000 2.555836 2.260075           0.295761\n",
      "0.250000 2.640066 2.334712           0.305354\n",
      "0.260000 2.721689 2.407054           0.314635\n",
      "0.270000 2.800627 2.477030           0.323597\n",
      "0.280000 2.876801 2.544570           0.332231\n",
      "0.290000 2.950136 2.609607           0.340529\n",
      "0.300000 3.020559 2.672077           0.348483\n",
      "0.310000 3.088002 2.731917           0.356085\n",
      "0.320000 3.152397 2.789069           0.363328\n",
      "0.330000 3.213681 2.843475           0.370206\n",
      "0.340000 3.271793 2.895081           0.376712\n",
      "0.350000 3.326677 2.943837           0.382840\n",
      "0.360000 3.378277 2.989693           0.388584\n",
      "0.370000 3.426544 3.032605           0.393939\n",
      "0.380000 3.471429 3.072528           0.398901\n",
      "0.390000 3.512888 3.109424           0.403464\n",
      "0.400000 3.550880 3.143256           0.407625\n",
      "0.410000 3.585369 3.173989           0.411379\n",
      "0.420000 3.616318 3.201594           0.414724\n",
      "0.430000 3.643699 3.226042           0.417657\n",
      "0.440000 3.667484 3.247310           0.420175\n",
      "0.450000 3.687650 3.265374           0.422275\n",
      "0.460000 3.704176 3.280219           0.423957\n",
      "0.470000 3.717047 3.291827           0.425219\n",
      "0.480000 3.726249 3.300188           0.426061\n",
      "0.490000 3.731774 3.305293           0.426481\n",
      "0.500000 3.733617 3.307136           0.426480\n",
      "0.510000 3.731774 3.305716           0.426058\n",
      "0.520000 3.726249 3.301033           0.425217\n",
      "0.530000 3.717047 3.293091           0.423956\n",
      "0.540000 3.704176 3.281897           0.422279\n",
      "0.550000 3.687650 3.267464           0.420186\n",
      "0.560000 3.667484 3.249803           0.417681\n",
      "0.570000 3.643699 3.228933           0.414766\n",
      "0.580000 3.616318 3.204874           0.411445\n",
      "0.590000 3.585369 3.177648           0.407720\n",
      "0.600000 3.550880 3.147283           0.403598\n",
      "0.610000 3.512888 3.113808           0.399080\n",
      "0.620000 3.471429 3.077255           0.394174\n",
      "0.630000 3.426544 3.037661           0.388883\n",
      "0.640000 3.378277 2.995063           0.383214\n",
      "0.650000 3.326677 2.949505           0.377172\n",
      "0.660000 3.271793 2.901029           0.370764\n",
      "0.670000 3.213681 2.849685           0.363996\n",
      "0.680000 3.152397 2.795521           0.356876\n",
      "0.690000 3.088002 2.738592           0.349410\n",
      "0.700000 3.020559 2.678952           0.341607\n",
      "0.710000 2.950136 2.616661           0.333475\n",
      "0.720000 2.876801 2.551780           0.325021\n",
      "0.730000 2.800627 2.484372           0.316255\n",
      "0.740000 2.721689 2.414503           0.307186\n",
      "0.750000 2.640066 2.342243           0.297823\n",
      "0.760000 2.555836 2.267662           0.288175\n",
      "0.770000 2.469085 2.190833           0.278252\n",
      "0.780000 2.379897 2.111833           0.268064\n",
      "0.790000 2.288360 2.030738           0.257622\n",
      "0.800000 2.194565 1.947628           0.246937\n",
      "0.810000 2.098604 1.862585           0.236018\n",
      "0.820000 2.000572 1.775694           0.224878\n",
      "0.830000 1.900566 1.687039           0.213527\n",
      "0.840000 1.798684 1.596707           0.201977\n",
      "0.850000 1.695026 1.504788           0.190239\n",
      "0.860000 1.589697 1.411372           0.178325\n",
      "0.870000 1.482798 1.316550           0.166248\n",
      "0.880000 1.374436 1.220418           0.154018\n",
      "0.890000 1.264718 1.123068           0.141650\n",
      "0.900000 1.153751 1.024597           0.129154\n",
      "0.910000 1.041646 0.925102           0.116544\n",
      "0.920000 0.928513 0.824681           0.103832\n",
      "0.930000 0.814463 0.723433           0.091031\n",
      "0.940000 0.699610 0.621457           0.078153\n",
      "0.950000 0.584066 0.518855           0.065211\n",
      "0.960000 0.467946 0.415727           0.052219\n",
      "0.970000 0.351364 0.312176           0.039189\n",
      "0.980000 0.234436 0.208302           0.026133\n",
      "0.990000 0.117276 0.104210           0.013066\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.7000000000000001\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.121116 0.107657           0.013460\n",
      "0.020000 0.242113 0.215221           0.026892\n",
      "0.030000 0.362871 0.322588           0.040283\n",
      "0.040000 0.483271 0.429650           0.053621\n",
      "0.050000 0.603194 0.536302           0.066891\n",
      "0.060000 0.722521 0.642439           0.080082\n",
      "0.070000 0.841136 0.747956           0.093180\n",
      "0.080000 0.958920 0.852748           0.106172\n",
      "0.090000 1.075758 0.956713           0.119046\n",
      "0.100000 1.191535 1.059746           0.131789\n",
      "0.110000 1.306135 1.161747           0.144389\n",
      "0.120000 1.419447 1.262614           0.156833\n",
      "0.130000 1.531357 1.362247           0.169110\n",
      "0.140000 1.641757 1.460549           0.181208\n",
      "0.150000 1.750536 1.557422           0.193114\n",
      "0.160000 1.857588 1.652770           0.204818\n",
      "0.170000 1.962806 1.746498           0.216308\n",
      "0.180000 2.066088 1.838515           0.227573\n",
      "0.190000 2.167330 1.928728           0.238602\n",
      "0.200000 2.266434 2.017049           0.249384\n",
      "0.210000 2.363300 2.103391           0.259910\n",
      "0.220000 2.457835 2.187666           0.270169\n",
      "0.230000 2.549944 2.269793           0.280151\n",
      "0.240000 2.639536 2.349690           0.289846\n",
      "0.250000 2.726524 2.427278           0.299246\n",
      "0.260000 2.810821 2.502479           0.308342\n",
      "0.270000 2.892344 2.575220           0.317124\n",
      "0.280000 2.971012 2.645428           0.325584\n",
      "0.290000 3.046749 2.713033           0.333716\n",
      "0.300000 3.119478 2.777969           0.341510\n",
      "0.310000 3.189129 2.840170           0.348959\n",
      "0.320000 3.255633 2.899576           0.356057\n",
      "0.330000 3.318924 2.956128           0.362796\n",
      "0.340000 3.378940 3.009768           0.369171\n",
      "0.350000 3.435621 3.060445           0.375176\n",
      "0.360000 3.488911 3.108106           0.380805\n",
      "0.370000 3.538758 3.152706           0.386052\n",
      "0.380000 3.585113 3.194200           0.390914\n",
      "0.390000 3.627930 3.232545           0.395385\n",
      "0.400000 3.667167 3.267705           0.399462\n",
      "0.410000 3.702784 3.299644           0.403140\n",
      "0.420000 3.734747 3.328330           0.406418\n",
      "0.430000 3.763025 3.353734           0.409291\n",
      "0.440000 3.787589 3.375831           0.411757\n",
      "0.450000 3.808415 3.394599           0.413815\n",
      "0.460000 3.825482 3.410019           0.415463\n",
      "0.470000 3.838775 3.422075           0.416699\n",
      "0.480000 3.848279 3.430755           0.417523\n",
      "0.490000 3.853985 3.436050           0.417934\n",
      "0.500000 3.855887 3.437955           0.417933\n",
      "0.510000 3.853985 3.436466           0.417519\n",
      "0.520000 3.848279 3.431585           0.416693\n",
      "0.530000 3.838775 3.423317           0.415457\n",
      "0.540000 3.825482 3.411670           0.413813\n",
      "0.550000 3.808415 3.396654           0.411761\n",
      "0.560000 3.787589 3.378283           0.409306\n",
      "0.570000 3.763025 3.356576           0.406449\n",
      "0.580000 3.734747 3.331554           0.403193\n",
      "0.590000 3.702784 3.303241           0.399543\n",
      "0.600000 3.667167 3.271664           0.395502\n",
      "0.610000 3.627930 3.236855           0.391075\n",
      "0.620000 3.585113 3.198847           0.386267\n",
      "0.630000 3.538758 3.157677           0.381081\n",
      "0.640000 3.488911 3.113386           0.375525\n",
      "0.650000 3.435621 3.066017           0.369604\n",
      "0.660000 3.378940 3.015616           0.363324\n",
      "0.670000 3.318924 2.962233           0.356691\n",
      "0.680000 3.255633 2.905920           0.349713\n",
      "0.690000 3.189129 2.846733           0.342397\n",
      "0.700000 3.119478 2.784728           0.334750\n",
      "0.710000 3.046749 2.719968           0.326780\n",
      "0.720000 2.971012 2.652516           0.318496\n",
      "0.730000 2.892344 2.582438           0.309906\n",
      "0.740000 2.810821 2.509803           0.301018\n",
      "0.750000 2.726524 2.434682           0.291842\n",
      "0.760000 2.639536 2.357149           0.282387\n",
      "0.770000 2.549944 2.277281           0.272663\n",
      "0.780000 2.457835 2.195155           0.262680\n",
      "0.790000 2.363300 2.110853           0.252447\n",
      "0.800000 2.266434 2.024458           0.241976\n",
      "0.810000 2.167330 1.936054           0.231277\n",
      "0.820000 2.066088 1.845728           0.220360\n",
      "0.830000 1.962806 1.753570           0.209236\n",
      "0.840000 1.857588 1.659670           0.197918\n",
      "0.850000 1.750536 1.564121           0.186415\n",
      "0.860000 1.641757 1.467016           0.174741\n",
      "0.870000 1.531357 1.368452           0.162906\n",
      "0.880000 1.419447 1.268524           0.150922\n",
      "0.890000 1.306135 1.167333           0.138802\n",
      "0.900000 1.191535 1.064977           0.126558\n",
      "0.910000 1.075758 0.961558           0.114201\n",
      "0.920000 0.958920 0.857176           0.101744\n",
      "0.930000 0.841136 0.751936           0.089200\n",
      "0.940000 0.722521 0.645940           0.076581\n",
      "0.950000 0.603194 0.539294           0.063899\n",
      "0.960000 0.483271 0.432102           0.051168\n",
      "0.970000 0.362871 0.324471           0.038400\n",
      "0.980000 0.242113 0.216506           0.025608\n",
      "0.990000 0.121116 0.108313           0.012803\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.71\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.125077 0.111906           0.013170\n",
      "0.020000 0.250030 0.223716           0.026314\n",
      "0.030000 0.374736 0.335319           0.039417\n",
      "0.040000 0.499072 0.446605           0.052468\n",
      "0.050000 0.622916 0.557464           0.065453\n",
      "0.060000 0.746146 0.667786           0.078359\n",
      "0.070000 0.868638 0.777463           0.091175\n",
      "0.080000 0.990274 0.886386           0.103888\n",
      "0.090000 1.110932 0.994448           0.116484\n",
      "0.100000 1.230494 1.101541           0.128953\n",
      "0.110000 1.348842 1.207560           0.141282\n",
      "0.120000 1.465859 1.312400           0.153458\n",
      "0.130000 1.581428 1.415958           0.165471\n",
      "0.140000 1.695438 1.518130           0.177308\n",
      "0.150000 1.807774 1.618816           0.188958\n",
      "0.160000 1.918326 1.717917           0.200409\n",
      "0.170000 2.026984 1.815333           0.211651\n",
      "0.180000 2.133643 1.910970           0.222673\n",
      "0.190000 2.238196 2.004731           0.233464\n",
      "0.200000 2.340540 2.096525           0.244014\n",
      "0.210000 2.440574 2.186261           0.254313\n",
      "0.220000 2.538199 2.273849           0.264350\n",
      "0.230000 2.633320 2.359203           0.274117\n",
      "0.240000 2.725842 2.442239           0.283603\n",
      "0.250000 2.815674 2.522873           0.292800\n",
      "0.260000 2.902727 2.601027           0.301699\n",
      "0.270000 2.986915 2.676623           0.310292\n",
      "0.280000 3.068156 2.749586           0.318570\n",
      "0.290000 3.146369 2.819843           0.326525\n",
      "0.300000 3.221476 2.887326           0.334151\n",
      "0.310000 3.293405 2.951966           0.341439\n",
      "0.320000 3.362083 3.013700           0.348383\n",
      "0.330000 3.427444 3.072467           0.354977\n",
      "0.340000 3.489421 3.128207           0.361214\n",
      "0.350000 3.547956 3.180867           0.367089\n",
      "0.360000 3.602989 3.230393           0.372595\n",
      "0.370000 3.654466 3.276736           0.377729\n",
      "0.380000 3.702336 3.319851           0.382485\n",
      "0.390000 3.746553 3.359694           0.386859\n",
      "0.400000 3.787073 3.396225           0.390848\n",
      "0.410000 3.823855 3.429408           0.394446\n",
      "0.420000 3.856863 3.459211           0.397652\n",
      "0.430000 3.886065 3.485602           0.400463\n",
      "0.440000 3.911432 3.508556           0.402876\n",
      "0.450000 3.932939 3.528050           0.404889\n",
      "0.460000 3.950565 3.544065           0.406500\n",
      "0.470000 3.964292 3.556582           0.407709\n",
      "0.480000 3.974106 3.565592           0.408515\n",
      "0.490000 3.979999 3.571083           0.408916\n",
      "0.500000 3.981964 3.573050           0.408914\n",
      "0.510000 3.979999 3.571491           0.408508\n",
      "0.520000 3.974106 3.566406           0.407700\n",
      "0.530000 3.964292 3.557802           0.406490\n",
      "0.540000 3.950565 3.545684           0.404880\n",
      "0.550000 3.932939 3.530066           0.402873\n",
      "0.560000 3.911432 3.510963           0.400469\n",
      "0.570000 3.886065 3.488392           0.397673\n",
      "0.580000 3.856863 3.462375           0.394488\n",
      "0.590000 3.823855 3.432939           0.390916\n",
      "0.600000 3.787073 3.400111           0.386962\n",
      "0.610000 3.746553 3.363924           0.382629\n",
      "0.620000 3.702336 3.324412           0.377924\n",
      "0.630000 3.654466 3.281615           0.372850\n",
      "0.640000 3.602989 3.235575           0.367414\n",
      "0.650000 3.547956 3.186336           0.361620\n",
      "0.660000 3.489421 3.133947           0.355475\n",
      "0.670000 3.427444 3.078459           0.348985\n",
      "0.680000 3.362083 3.019926           0.342157\n",
      "0.690000 3.293405 2.958407           0.334998\n",
      "0.700000 3.221476 2.893960           0.327516\n",
      "0.710000 3.146369 2.826651           0.319718\n",
      "0.720000 3.068156 2.756543           0.311612\n",
      "0.730000 2.986915 2.683708           0.303207\n",
      "0.740000 2.902727 2.608216           0.294511\n",
      "0.750000 2.815674 2.530141           0.285533\n",
      "0.760000 2.725842 2.449560           0.276282\n",
      "0.770000 2.633320 2.366552           0.266768\n",
      "0.780000 2.538199 2.281199           0.257000\n",
      "0.790000 2.440574 2.193585           0.246989\n",
      "0.800000 2.340540 2.103796           0.236743\n",
      "0.810000 2.238196 2.011921           0.226275\n",
      "0.820000 2.133643 1.918049           0.215594\n",
      "0.830000 2.026984 1.822274           0.204711\n",
      "0.840000 1.918326 1.724689           0.193636\n",
      "0.850000 1.807774 1.625391           0.182383\n",
      "0.860000 1.695438 1.524477           0.170960\n",
      "0.870000 1.581428 1.422047           0.159381\n",
      "0.880000 1.465859 1.318202           0.147657\n",
      "0.890000 1.348842 1.213043           0.135799\n",
      "0.900000 1.230494 1.106676           0.123819\n",
      "0.910000 1.110932 0.999203           0.111729\n",
      "0.920000 0.990274 0.890732           0.099542\n",
      "0.930000 0.868638 0.781369           0.087269\n",
      "0.940000 0.746146 0.671222           0.074923\n",
      "0.950000 0.622916 0.560400           0.062516\n",
      "0.960000 0.499072 0.449012           0.050061\n",
      "0.970000 0.374736 0.337167           0.037569\n",
      "0.980000 0.250030 0.224976           0.025053\n",
      "0.990000 0.125077 0.112550           0.012526\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.72\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.129160 0.116294           0.012866\n",
      "0.020000 0.258193 0.232487           0.025705\n",
      "0.030000 0.386971 0.348465           0.038506\n",
      "0.040000 0.515367 0.464112           0.051255\n",
      "0.050000 0.643254 0.579315           0.063939\n",
      "0.060000 0.770506 0.693959           0.076548\n",
      "0.070000 0.896999 0.807932           0.089067\n",
      "0.080000 1.022605 0.921120           0.101485\n",
      "0.090000 1.147203 1.033412           0.113791\n",
      "0.100000 1.270669 1.144698           0.125971\n",
      "0.110000 1.392880 1.254866           0.138014\n",
      "0.120000 1.513717 1.363809           0.149909\n",
      "0.130000 1.633060 1.471417           0.161643\n",
      "0.140000 1.750792 1.577586           0.173206\n",
      "0.150000 1.866796 1.682209           0.184586\n",
      "0.160000 1.980957 1.785184           0.195773\n",
      "0.170000 2.093163 1.886409           0.206754\n",
      "0.180000 2.203304 1.985783           0.217521\n",
      "0.190000 2.311270 2.083208           0.228062\n",
      "0.200000 2.416956 2.178588           0.238367\n",
      "0.210000 2.520256 2.271829           0.248427\n",
      "0.220000 2.621069 2.362837           0.258232\n",
      "0.230000 2.719295 2.451523           0.267772\n",
      "0.240000 2.814838 2.537799           0.277038\n",
      "0.250000 2.907602 2.621580           0.286022\n",
      "0.260000 2.997498 2.702783           0.294714\n",
      "0.270000 3.084435 2.781327           0.303108\n",
      "0.280000 3.168328 2.857134           0.311193\n",
      "0.290000 3.249094 2.930130           0.318964\n",
      "0.300000 3.326654 3.000242           0.326413\n",
      "0.310000 3.400931 3.067399           0.333532\n",
      "0.320000 3.471852 3.131537           0.340315\n",
      "0.330000 3.539346 3.192591           0.346755\n",
      "0.340000 3.603347 3.250500           0.352847\n",
      "0.350000 3.663793 3.305207           0.358585\n",
      "0.360000 3.720622 3.356658           0.363964\n",
      "0.370000 3.773780 3.404802           0.368978\n",
      "0.380000 3.823214 3.449590           0.373623\n",
      "0.390000 3.868874 3.490979           0.377896\n",
      "0.400000 3.910716 3.528926           0.381791\n",
      "0.410000 3.948699 3.563394           0.385305\n",
      "0.420000 3.982785 3.594349           0.388437\n",
      "0.430000 4.012941 3.621760           0.391181\n",
      "0.440000 4.039136 3.645599           0.393538\n",
      "0.450000 4.061345 3.665842           0.395503\n",
      "0.460000 4.079546 3.682470           0.397077\n",
      "0.470000 4.093722 3.695464           0.398257\n",
      "0.480000 4.103857 3.704813           0.399043\n",
      "0.490000 4.109942 3.710506           0.399435\n",
      "0.500000 4.111971 3.712538           0.399432\n",
      "0.510000 4.109942 3.710906           0.399035\n",
      "0.520000 4.103857 3.705611           0.398245\n",
      "0.530000 4.093722 3.696659           0.397063\n",
      "0.540000 4.079546 3.684057           0.395490\n",
      "0.550000 4.061345 3.667817           0.393528\n",
      "0.560000 4.039136 3.647956           0.391180\n",
      "0.570000 4.012941 3.624493           0.388448\n",
      "0.580000 3.982785 3.597450           0.385336\n",
      "0.590000 3.948699 3.566853           0.381846\n",
      "0.600000 3.910716 3.532733           0.377983\n",
      "0.610000 3.868874 3.495123           0.373751\n",
      "0.620000 3.823214 3.454059           0.369154\n",
      "0.630000 3.773780 3.409582           0.364198\n",
      "0.640000 3.720622 3.361736           0.358887\n",
      "0.650000 3.663793 3.310566           0.353227\n",
      "0.660000 3.603347 3.256124           0.347224\n",
      "0.670000 3.539346 3.198462           0.340884\n",
      "0.680000 3.471852 3.137638           0.334214\n",
      "0.690000 3.400931 3.073710           0.327221\n",
      "0.700000 3.326654 3.006742           0.319912\n",
      "0.710000 3.249094 2.936800           0.312295\n",
      "0.720000 3.168328 2.863951           0.304377\n",
      "0.730000 3.084435 2.788269           0.296166\n",
      "0.740000 2.997498 2.709826           0.287672\n",
      "0.750000 2.907602 2.628701           0.278902\n",
      "0.760000 2.814838 2.544972           0.269865\n",
      "0.770000 2.719295 2.458723           0.260572\n",
      "0.780000 2.621069 2.370038           0.251030\n",
      "0.790000 2.520256 2.279005           0.241251\n",
      "0.800000 2.416956 2.185712           0.231243\n",
      "0.810000 2.311270 2.090253           0.221018\n",
      "0.820000 2.203304 1.992720           0.210584\n",
      "0.830000 2.093163 1.893210           0.199954\n",
      "0.840000 1.980957 1.791820           0.189137\n",
      "0.850000 1.866796 1.688651           0.178144\n",
      "0.860000 1.750792 1.583805           0.166987\n",
      "0.870000 1.633060 1.477384           0.155677\n",
      "0.880000 1.513717 1.369493           0.144225\n",
      "0.890000 1.392880 1.260238           0.132642\n",
      "0.900000 1.270669 1.149728           0.120940\n",
      "0.910000 1.147203 1.038072           0.109132\n",
      "0.920000 1.022605 0.925378           0.097228\n",
      "0.930000 0.896999 0.811759           0.085240\n",
      "0.940000 0.770506 0.697326           0.073181\n",
      "0.950000 0.643254 0.582192           0.061062\n",
      "0.960000 0.515367 0.466470           0.048896\n",
      "0.970000 0.386971 0.350276           0.036695\n",
      "0.980000 0.258193 0.233722           0.024470\n",
      "0.990000 0.129160 0.116925           0.012235\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.73\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.133371 0.120824           0.012547\n",
      "0.020000 0.266611 0.241543           0.025068\n",
      "0.030000 0.399587 0.362037           0.037551\n",
      "0.040000 0.532169 0.482186           0.049983\n",
      "0.050000 0.664226 0.601873           0.062353\n",
      "0.060000 0.795628 0.720979           0.074649\n",
      "0.070000 0.926244 0.839387           0.086857\n",
      "0.080000 1.055946 0.956979           0.098967\n",
      "0.090000 1.184606 1.073639           0.110967\n",
      "0.100000 1.312097 1.189252           0.122845\n",
      "0.110000 1.438293 1.303704           0.134589\n",
      "0.120000 1.563070 1.416882           0.146188\n",
      "0.130000 1.686304 1.528673           0.157631\n",
      "0.140000 1.807874 1.638967           0.168907\n",
      "0.150000 1.927660 1.747656           0.180004\n",
      "0.160000 2.045544 1.854631           0.190913\n",
      "0.170000 2.161408 1.959787           0.201621\n",
      "0.180000 2.275140 2.063020           0.212120\n",
      "0.190000 2.386626 2.164227           0.222399\n",
      "0.200000 2.495757 2.263309           0.232449\n",
      "0.210000 2.602425 2.360167           0.242258\n",
      "0.220000 2.706525 2.454706           0.251819\n",
      "0.230000 2.807954 2.546832           0.261122\n",
      "0.240000 2.906612 2.636454           0.270158\n",
      "0.250000 3.002401 2.723483           0.278918\n",
      "0.260000 3.095227 2.807833           0.287394\n",
      "0.270000 3.184999 2.889421           0.295578\n",
      "0.280000 3.271627 2.968164           0.303463\n",
      "0.290000 3.355027 3.043987           0.311040\n",
      "0.300000 3.435115 3.116813           0.318303\n",
      "0.310000 3.511814 3.186570           0.325244\n",
      "0.320000 3.585047 3.253189           0.331858\n",
      "0.330000 3.654742 3.316603           0.338138\n",
      "0.340000 3.720830 3.376751           0.344078\n",
      "0.350000 3.783246 3.433573           0.349673\n",
      "0.360000 3.841928 3.487011           0.354918\n",
      "0.370000 3.896819 3.537012           0.359807\n",
      "0.380000 3.947865 3.583528           0.364336\n",
      "0.390000 3.995014 3.626512           0.368502\n",
      "0.400000 4.038220 3.665921           0.372299\n",
      "0.410000 4.077442 3.701716           0.375726\n",
      "0.420000 4.112639 3.733860           0.378779\n",
      "0.430000 4.143778 3.762323           0.381455\n",
      "0.440000 4.170827 3.787075           0.383752\n",
      "0.450000 4.193760 3.808092           0.385668\n",
      "0.460000 4.212555 3.825353           0.387202\n",
      "0.470000 4.227192 3.838840           0.388352\n",
      "0.480000 4.237658 3.848539           0.389119\n",
      "0.490000 4.243941 3.854441           0.389500\n",
      "0.500000 4.246036 3.856540           0.389497\n",
      "0.510000 4.243941 3.854832           0.389109\n",
      "0.520000 4.237658 3.849320           0.388338\n",
      "0.530000 4.227192 3.840008           0.387184\n",
      "0.540000 4.212555 3.826905           0.385650\n",
      "0.550000 4.193760 3.810024           0.383736\n",
      "0.560000 4.170827 3.789381           0.381446\n",
      "0.570000 4.143778 3.764996           0.378782\n",
      "0.580000 4.112639 3.736893           0.375746\n",
      "0.590000 4.077442 3.705099           0.372343\n",
      "0.600000 4.038220 3.669645           0.368576\n",
      "0.610000 3.995014 3.630566           0.364448\n",
      "0.620000 3.947865 3.587899           0.359965\n",
      "0.630000 3.896819 3.541688           0.355132\n",
      "0.640000 3.841928 3.491976           0.349952\n",
      "0.650000 3.783246 3.438813           0.344433\n",
      "0.660000 3.720830 3.382251           0.338579\n",
      "0.670000 3.654742 3.322346           0.332396\n",
      "0.680000 3.585047 3.259155           0.325892\n",
      "0.690000 3.511814 3.192741           0.319073\n",
      "0.700000 3.435115 3.123170           0.311945\n",
      "0.710000 3.355027 3.050510           0.304517\n",
      "0.720000 3.271627 2.974831           0.296796\n",
      "0.730000 3.184999 2.896209           0.288789\n",
      "0.740000 3.095227 2.814721           0.280506\n",
      "0.750000 3.002401 2.730447           0.271954\n",
      "0.760000 2.906612 2.643469           0.263142\n",
      "0.770000 2.807954 2.553874           0.254080\n",
      "0.780000 2.706525 2.461749           0.244776\n",
      "0.790000 2.602425 2.367186           0.235240\n",
      "0.800000 2.495757 2.270276           0.225481\n",
      "0.810000 2.386626 2.171116           0.215510\n",
      "0.820000 2.275140 2.069804           0.205336\n",
      "0.830000 2.161408 1.966438           0.194970\n",
      "0.840000 2.045544 1.861121           0.184423\n",
      "0.850000 1.927660 1.753956           0.173704\n",
      "0.860000 1.807874 1.645049           0.162825\n",
      "0.870000 1.686304 1.534508           0.151796\n",
      "0.880000 1.563070 1.422441           0.140629\n",
      "0.890000 1.438293 1.308958           0.129335\n",
      "0.900000 1.312097 1.194172           0.117925\n",
      "0.910000 1.184606 1.078196           0.106411\n",
      "0.920000 1.055946 0.961143           0.094803\n",
      "0.930000 0.926244 0.843130           0.083114\n",
      "0.940000 0.795628 0.724272           0.071356\n",
      "0.950000 0.664226 0.604687           0.059539\n",
      "0.960000 0.532169 0.484493           0.047677\n",
      "0.970000 0.399587 0.363808           0.035780\n",
      "0.980000 0.266611 0.242751           0.023860\n",
      "0.990000 0.133371 0.121442           0.011929\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.74\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.137714 0.125501           0.012213\n",
      "0.020000 0.275292 0.250890           0.024402\n",
      "0.030000 0.412598 0.376046           0.036553\n",
      "0.040000 0.549498 0.500843           0.048655\n",
      "0.050000 0.685854 0.625159           0.060696\n",
      "0.060000 0.821535 0.748871           0.072664\n",
      "0.070000 0.956404 0.871856           0.084548\n",
      "0.080000 1.090329 0.993993           0.096336\n",
      "0.090000 1.223179 1.115162           0.108016\n",
      "0.100000 1.354821 1.235243           0.119578\n",
      "0.110000 1.485126 1.354116           0.131010\n",
      "0.120000 1.613966 1.471665           0.142300\n",
      "0.130000 1.741213 1.587774           0.153439\n",
      "0.140000 1.866741 1.702327           0.164414\n",
      "0.150000 1.990427 1.815211           0.175216\n",
      "0.160000 2.112149 1.926315           0.185834\n",
      "0.170000 2.231787 2.035529           0.196258\n",
      "0.180000 2.349221 2.142744           0.206477\n",
      "0.190000 2.464338 2.247856           0.216482\n",
      "0.200000 2.577023 2.350759           0.226264\n",
      "0.210000 2.687164 2.451352           0.235812\n",
      "0.220000 2.794653 2.549535           0.245118\n",
      "0.230000 2.899385 2.645212           0.254173\n",
      "0.240000 3.001255 2.738287           0.262968\n",
      "0.250000 3.100163 2.828669           0.271495\n",
      "0.260000 3.196012 2.916267           0.279745\n",
      "0.270000 3.288706 3.000996           0.287711\n",
      "0.280000 3.378156 3.082771           0.295385\n",
      "0.290000 3.464271 3.161511           0.302760\n",
      "0.300000 3.546967 3.237138           0.309829\n",
      "0.310000 3.626163 3.309578           0.316585\n",
      "0.320000 3.701781 3.378758           0.323023\n",
      "0.330000 3.773745 3.444610           0.329135\n",
      "0.340000 3.841985 3.507068           0.334917\n",
      "0.350000 3.906433 3.566071           0.340362\n",
      "0.360000 3.967027 3.621560           0.345466\n",
      "0.370000 4.023705 3.673480           0.350225\n",
      "0.380000 4.076412 3.721779           0.354633\n",
      "0.390000 4.125097 3.766410           0.358687\n",
      "0.400000 4.169710 3.807327           0.362383\n",
      "0.410000 4.210209 3.844491           0.365718\n",
      "0.420000 4.246552 3.877863           0.368689\n",
      "0.430000 4.278705 3.907412           0.371293\n",
      "0.440000 4.306635 3.933106           0.373528\n",
      "0.450000 4.330315 3.954922           0.375393\n",
      "0.460000 4.349721 3.972836           0.376886\n",
      "0.470000 4.364835 3.986830           0.378005\n",
      "0.480000 4.375641 3.996892           0.378750\n",
      "0.490000 4.382129 4.003009           0.379120\n",
      "0.500000 4.384293 4.005176           0.379117\n",
      "0.510000 4.382129 4.003390           0.378739\n",
      "0.520000 4.375641 3.997654           0.377988\n",
      "0.530000 4.364835 3.987971           0.376864\n",
      "0.540000 4.349721 3.974351           0.375370\n",
      "0.550000 4.330315 3.956807           0.373507\n",
      "0.560000 4.306635 3.935357           0.371278\n",
      "0.570000 4.278705 3.910021           0.368684\n",
      "0.580000 4.246552 3.880823           0.365729\n",
      "0.590000 4.210209 3.847793           0.362415\n",
      "0.600000 4.169710 3.810962           0.358748\n",
      "0.610000 4.125097 3.770366           0.354730\n",
      "0.620000 4.076412 3.726046           0.350366\n",
      "0.630000 4.023705 3.678044           0.345661\n",
      "0.640000 3.967027 3.626407           0.340619\n",
      "0.650000 3.906433 3.571187           0.335246\n",
      "0.660000 3.841985 3.512437           0.329548\n",
      "0.670000 3.773745 3.450215           0.323530\n",
      "0.680000 3.701781 3.384582           0.317199\n",
      "0.690000 3.626163 3.315602           0.310561\n",
      "0.700000 3.546967 3.243344           0.303623\n",
      "0.710000 3.464271 3.167878           0.296393\n",
      "0.720000 3.378156 3.089278           0.288877\n",
      "0.730000 3.288706 3.007623           0.281084\n",
      "0.740000 3.196012 2.922991           0.273021\n",
      "0.750000 3.100163 2.835466           0.264697\n",
      "0.760000 3.001255 2.745135           0.256120\n",
      "0.770000 2.899385 2.652086           0.247299\n",
      "0.780000 2.794653 2.556410           0.238243\n",
      "0.790000 2.687164 2.458203           0.228961\n",
      "0.800000 2.577023 2.357560           0.219463\n",
      "0.810000 2.464338 2.254581           0.209757\n",
      "0.820000 2.349221 2.149366           0.199855\n",
      "0.830000 2.231787 2.042021           0.189766\n",
      "0.840000 2.112149 1.932650           0.179499\n",
      "0.850000 1.990427 1.821361           0.169066\n",
      "0.860000 1.866741 1.708264           0.158477\n",
      "0.870000 1.741213 1.593470           0.147743\n",
      "0.880000 1.613966 1.477092           0.136874\n",
      "0.890000 1.485126 1.359245           0.125881\n",
      "0.900000 1.354821 1.240045           0.114776\n",
      "0.910000 1.223179 1.119610           0.103569\n",
      "0.920000 1.090329 0.998058           0.092271\n",
      "0.930000 0.956404 0.875509           0.080894\n",
      "0.940000 0.821535 0.752085           0.069450\n",
      "0.950000 0.685854 0.627905           0.057949\n",
      "0.960000 0.549498 0.503094           0.046403\n",
      "0.970000 0.412598 0.377775           0.034824\n",
      "0.980000 0.275292 0.252069           0.023223\n",
      "0.990000 0.137714 0.126103           0.011611\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.75\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.142193 0.130327           0.011866\n",
      "0.020000 0.284245 0.260538           0.023707\n",
      "0.030000 0.426017 0.390504           0.035512\n",
      "0.040000 0.567368 0.520098           0.047270\n",
      "0.050000 0.708160 0.649191           0.058968\n",
      "0.060000 0.848252 0.777656           0.070596\n",
      "0.070000 0.987508 0.905366           0.082141\n",
      "0.080000 1.125788 1.032195           0.093594\n",
      "0.090000 1.262958 1.158017           0.104942\n",
      "0.100000 1.398882 1.282708           0.116174\n",
      "0.110000 1.533425 1.406145           0.127280\n",
      "0.120000 1.666454 1.528206           0.138249\n",
      "0.130000 1.797840 1.648770           0.149070\n",
      "0.140000 1.927450 1.767718           0.159733\n",
      "0.150000 2.055159 1.884932           0.170227\n",
      "0.160000 2.180839 2.000297           0.180542\n",
      "0.170000 2.304368 2.113699           0.190669\n",
      "0.180000 2.425622 2.225025           0.200597\n",
      "0.190000 2.544482 2.334165           0.210317\n",
      "0.200000 2.660831 2.441012           0.219819\n",
      "0.210000 2.774555 2.545459           0.229095\n",
      "0.220000 2.885540 2.647404           0.238136\n",
      "0.230000 2.993677 2.746745           0.246932\n",
      "0.240000 3.098860 2.843384           0.255476\n",
      "0.250000 3.200985 2.937225           0.263760\n",
      "0.260000 3.299951 3.028177           0.271775\n",
      "0.270000 3.395660 3.116147           0.279513\n",
      "0.280000 3.488018 3.201050           0.286968\n",
      "0.290000 3.576934 3.282802           0.294133\n",
      "0.300000 3.662320 3.361320           0.301000\n",
      "0.310000 3.744092 3.436528           0.307563\n",
      "0.320000 3.822168 3.508352           0.313817\n",
      "0.330000 3.896473 3.576719           0.319755\n",
      "0.340000 3.966932 3.641561           0.325371\n",
      "0.350000 4.033477 3.702816           0.330661\n",
      "0.360000 4.096041 3.760422           0.335619\n",
      "0.370000 4.154562 3.814321           0.340241\n",
      "0.380000 4.208984 3.864460           0.344523\n",
      "0.390000 4.259251 3.910790           0.348461\n",
      "0.400000 4.305316 3.953264           0.352051\n",
      "0.410000 4.347131 3.991840           0.355291\n",
      "0.420000 4.384657 4.026480           0.358176\n",
      "0.430000 4.417855 4.057149           0.360706\n",
      "0.440000 4.446693 4.083816           0.362877\n",
      "0.450000 4.471143 4.106455           0.364688\n",
      "0.460000 4.491181 4.125044           0.366137\n",
      "0.470000 4.506786 4.139562           0.367224\n",
      "0.480000 4.517944 4.149997           0.367947\n",
      "0.490000 4.524643 4.156336           0.368307\n",
      "0.500000 4.526877 4.158574           0.368303\n",
      "0.510000 4.524643 4.156708           0.367935\n",
      "0.520000 4.517944 4.150739           0.367205\n",
      "0.530000 4.506786 4.140673           0.366113\n",
      "0.540000 4.491181 4.126520           0.364661\n",
      "0.550000 4.471143 4.108292           0.362851\n",
      "0.560000 4.446693 4.086009           0.360684\n",
      "0.570000 4.417855 4.059691           0.358164\n",
      "0.580000 4.384657 4.029364           0.355293\n",
      "0.590000 4.347131 3.995057           0.352074\n",
      "0.600000 4.305316 3.956805           0.348510\n",
      "0.610000 4.259251 3.914644           0.344607\n",
      "0.620000 4.208984 3.868617           0.340367\n",
      "0.630000 4.154562 3.818767           0.335795\n",
      "0.640000 4.096041 3.765143           0.330897\n",
      "0.650000 4.033477 3.707800           0.325677\n",
      "0.660000 3.966932 3.646791           0.320141\n",
      "0.670000 3.896473 3.582179           0.314294\n",
      "0.680000 3.822168 3.514025           0.308144\n",
      "0.690000 3.744092 3.442397           0.301695\n",
      "0.700000 3.662320 3.367366           0.294955\n",
      "0.710000 3.576934 3.289004           0.287930\n",
      "0.720000 3.488018 3.207390           0.280629\n",
      "0.730000 3.395660 3.122603           0.273058\n",
      "0.740000 3.299951 3.034726           0.265225\n",
      "0.750000 3.200985 2.943847           0.257138\n",
      "0.760000 3.098860 2.850055           0.248806\n",
      "0.770000 2.993677 2.753441           0.240236\n",
      "0.780000 2.885540 2.654101           0.231439\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.790000 2.774555 2.552133           0.222421\n",
      "0.800000 2.660831 2.447637           0.213194\n",
      "0.810000 2.544482 2.340717           0.203766\n",
      "0.820000 2.425622 2.231476           0.194146\n",
      "0.830000 2.304368 2.120023           0.184344\n",
      "0.840000 2.180839 2.006468           0.174371\n",
      "0.850000 2.055159 1.890923           0.164236\n",
      "0.860000 1.927450 1.773501           0.153949\n",
      "0.870000 1.797840 1.654318           0.143521\n",
      "0.880000 1.666454 1.533492           0.132963\n",
      "0.890000 1.533425 1.411141           0.122284\n",
      "0.900000 1.398882 1.287386           0.111496\n",
      "0.910000 1.262958 1.162350           0.100609\n",
      "0.920000 1.125788 1.036155           0.089634\n",
      "0.930000 0.987508 0.908925           0.078582\n",
      "0.940000 0.848252 0.780787           0.067465\n",
      "0.950000 0.708160 0.651867           0.056293\n",
      "0.960000 0.567368 0.522291           0.045077\n",
      "0.970000 0.426017 0.392188           0.033828\n",
      "0.980000 0.284245 0.261686           0.022559\n",
      "0.990000 0.142193 0.130914           0.011279\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.76\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.146812 0.135307           0.011505\n",
      "0.020000 0.293478 0.270493           0.022985\n",
      "0.030000 0.439856 0.405424           0.034431\n",
      "0.040000 0.585799 0.539968           0.045831\n",
      "0.050000 0.731164 0.673991           0.057173\n",
      "0.060000 0.875807 0.807361           0.068446\n",
      "0.070000 1.019586 0.939946           0.079640\n",
      "0.080000 1.162359 1.071615           0.090743\n",
      "0.090000 1.303985 1.202239           0.101746\n",
      "0.100000 1.444323 1.331688           0.112636\n",
      "0.110000 1.583237 1.459833           0.123403\n",
      "0.120000 1.720588 1.586550           0.134038\n",
      "0.130000 1.856241 1.711712           0.144529\n",
      "0.140000 1.990062 1.835195           0.154867\n",
      "0.150000 2.121919 1.956878           0.165041\n",
      "0.160000 2.251682 2.076640           0.175042\n",
      "0.170000 2.379223 2.194364           0.184860\n",
      "0.180000 2.504416 2.309931           0.194485\n",
      "0.190000 2.627138 2.423229           0.203909\n",
      "0.200000 2.747267 2.534145           0.213122\n",
      "0.210000 2.864684 2.642569           0.222115\n",
      "0.220000 2.979274 2.748395           0.230879\n",
      "0.230000 3.090925 2.851517           0.239408\n",
      "0.240000 3.199525 2.951834           0.247691\n",
      "0.250000 3.304967 3.049245           0.255721\n",
      "0.260000 3.407148 3.143656           0.263492\n",
      "0.270000 3.505966 3.234972           0.270994\n",
      "0.280000 3.601324 3.323103           0.278221\n",
      "0.290000 3.693128 3.407961           0.285167\n",
      "0.300000 3.781288 3.489463           0.291825\n",
      "0.310000 3.865716 3.567528           0.298188\n",
      "0.320000 3.946329 3.642079           0.304250\n",
      "0.330000 4.023047 3.713041           0.310006\n",
      "0.340000 4.095795 3.780344           0.315451\n",
      "0.350000 4.164501 3.843922           0.320579\n",
      "0.360000 4.229097 3.903712           0.325386\n",
      "0.370000 4.289520 3.959653           0.329867\n",
      "0.380000 4.345709 4.011692           0.334018\n",
      "0.390000 4.397610 4.059775           0.337835\n",
      "0.400000 4.445171 4.103855           0.341315\n",
      "0.410000 4.488344 4.143889           0.344455\n",
      "0.420000 4.527089 4.179836           0.347253\n",
      "0.430000 4.561366 4.211661           0.349704\n",
      "0.440000 4.591141 4.239332           0.351809\n",
      "0.450000 4.616385 4.262821           0.353564\n",
      "0.460000 4.637074 4.282105           0.354969\n",
      "0.470000 4.653186 4.297164           0.356022\n",
      "0.480000 4.664706 4.307983           0.356723\n",
      "0.490000 4.671623 4.314552           0.357071\n",
      "0.500000 4.673929 4.316863           0.357066\n",
      "0.510000 4.671623 4.314913           0.356710\n",
      "0.520000 4.664706 4.308705           0.356001\n",
      "0.530000 4.653186 4.298244           0.354942\n",
      "0.540000 4.637074 4.283540           0.353534\n",
      "0.550000 4.616385 4.264607           0.351778\n",
      "0.560000 4.591141 4.241463           0.349677\n",
      "0.570000 4.561366 4.214132           0.347234\n",
      "0.580000 4.527089 4.182639           0.344449\n",
      "0.590000 4.488344 4.147016           0.341328\n",
      "0.600000 4.445171 4.107297           0.337873\n",
      "0.610000 4.397610 4.063522           0.334088\n",
      "0.620000 4.345709 4.015732           0.329977\n",
      "0.630000 4.289520 3.963975           0.325545\n",
      "0.640000 4.229097 3.908302           0.320796\n",
      "0.650000 4.164501 3.848766           0.315735\n",
      "0.660000 4.095795 3.785428           0.310367\n",
      "0.670000 4.023047 3.718348           0.304699\n",
      "0.680000 3.946329 3.647594           0.298735\n",
      "0.690000 3.865716 3.573233           0.292483\n",
      "0.700000 3.781288 3.495340           0.285948\n",
      "0.710000 3.693128 3.413990           0.279138\n",
      "0.720000 3.601324 3.329265           0.272059\n",
      "0.730000 3.505966 3.241247           0.264719\n",
      "0.740000 3.407148 3.150023           0.257125\n",
      "0.750000 3.304967 3.055682           0.249285\n",
      "0.760000 3.199525 2.958318           0.241207\n",
      "0.770000 3.090925 2.858026           0.232899\n",
      "0.780000 2.979274 2.754905           0.224369\n",
      "0.790000 2.864684 2.649057           0.215627\n",
      "0.800000 2.747267 2.540585           0.206681\n",
      "0.810000 2.627138 2.429597           0.197541\n",
      "0.820000 2.504416 2.316202           0.188215\n",
      "0.830000 2.379223 2.200511           0.178712\n",
      "0.840000 2.251682 2.082639           0.169043\n",
      "0.850000 2.121919 1.962702           0.159218\n",
      "0.860000 1.990062 1.840817           0.149245\n",
      "0.870000 1.856241 1.717105           0.139136\n",
      "0.880000 1.720588 1.591688           0.128900\n",
      "0.890000 1.583237 1.464690           0.118547\n",
      "0.900000 1.444323 1.336235           0.108088\n",
      "0.910000 1.303985 1.206451           0.097534\n",
      "0.920000 1.162359 1.075464           0.086894\n",
      "0.930000 1.019586 0.943406           0.076180\n",
      "0.940000 0.875807 0.810404           0.065403\n",
      "0.950000 0.731164 0.676592           0.054572\n",
      "0.960000 0.585799 0.542100           0.043699\n",
      "0.970000 0.439856 0.407061           0.032794\n",
      "0.980000 0.293478 0.271609           0.021869\n",
      "0.990000 0.146812 0.135878           0.010934\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.77\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.151576 0.140446           0.011130\n",
      "0.020000 0.303002 0.280765           0.022237\n",
      "0.030000 0.454129 0.420818           0.033310\n",
      "0.040000 0.604807 0.560469           0.044338\n",
      "0.050000 0.754889 0.699578           0.055311\n",
      "0.060000 0.904226 0.838009           0.066217\n",
      "0.070000 1.052671 0.975624           0.077047\n",
      "0.080000 1.200077 1.112288           0.087788\n",
      "0.090000 1.346298 1.247866           0.098432\n",
      "0.100000 1.491191 1.382223           0.108967\n",
      "0.110000 1.634612 1.515228           0.119384\n",
      "0.120000 1.776420 1.646748           0.129672\n",
      "0.130000 1.916475 1.776653           0.139822\n",
      "0.140000 2.054638 1.904816           0.149822\n",
      "0.150000 2.190774 2.031109           0.159665\n",
      "0.160000 2.324748 2.155408           0.169340\n",
      "0.170000 2.456427 2.277590           0.178838\n",
      "0.180000 2.585683 2.397534           0.188149\n",
      "0.190000 2.712386 2.515121           0.197265\n",
      "0.200000 2.836413 2.630236           0.206178\n",
      "0.210000 2.957641 2.742763           0.214878\n",
      "0.220000 3.075950 2.852593           0.223356\n",
      "0.230000 3.191223 2.959617           0.231606\n",
      "0.240000 3.303347 3.063727           0.239619\n",
      "0.250000 3.412211 3.164823           0.247388\n",
      "0.260000 3.517707 3.262803           0.254905\n",
      "0.270000 3.619732 3.357570           0.262162\n",
      "0.280000 3.718185 3.449031           0.269154\n",
      "0.290000 3.812968 3.537095           0.275873\n",
      "0.300000 3.903988 3.621675           0.282313\n",
      "0.310000 3.991156 3.702688           0.288468\n",
      "0.320000 4.074384 3.780052           0.294332\n",
      "0.330000 4.153592 3.853691           0.299901\n",
      "0.340000 4.228701 3.923533           0.305167\n",
      "0.350000 4.299636 3.989508           0.310128\n",
      "0.360000 4.366329 4.051551           0.314777\n",
      "0.370000 4.428712 4.109600           0.319112\n",
      "0.380000 4.486724 4.163597           0.323127\n",
      "0.390000 4.540309 4.213490           0.326820\n",
      "0.400000 4.589413 4.259227           0.330186\n",
      "0.410000 4.633988 4.300765           0.333223\n",
      "0.420000 4.673990 4.338061           0.335929\n",
      "0.430000 4.709379 4.371078           0.338300\n",
      "0.440000 4.740120 4.399784           0.340336\n",
      "0.450000 4.766183 4.424150           0.342033\n",
      "0.460000 4.787543 4.444152           0.343392\n",
      "0.470000 4.804178 4.459768           0.344410\n",
      "0.480000 4.816072 4.470985           0.345087\n",
      "0.490000 4.823213 4.477790           0.345424\n",
      "0.500000 4.825595 4.480176           0.345419\n",
      "0.510000 4.823213 4.478140           0.345073\n",
      "0.520000 4.816072 4.471685           0.344388\n",
      "0.530000 4.804178 4.460816           0.343363\n",
      "0.540000 4.787543 4.445543           0.342000\n",
      "0.550000 4.766183 4.425882           0.340301\n",
      "0.560000 4.740120 4.401852           0.338268\n",
      "0.570000 4.709379 4.373475           0.335904\n",
      "0.580000 4.673990 4.340780           0.333210\n",
      "0.590000 4.633988 4.303798           0.330190\n",
      "0.600000 4.589413 4.262566           0.326848\n",
      "0.610000 4.540309 4.217123           0.323186\n",
      "0.620000 4.486724 4.167516           0.319209\n",
      "0.630000 4.428712 4.113791           0.314921\n",
      "0.640000 4.366329 4.056003           0.310326\n",
      "0.650000 4.299636 3.994207           0.305430\n",
      "0.660000 4.228701 3.928464           0.300237\n",
      "0.670000 4.153592 3.858839           0.294753\n",
      "0.680000 4.074384 3.785400           0.288984\n",
      "0.690000 3.991156 3.708220           0.282935\n",
      "0.700000 3.903988 3.627374           0.276614\n",
      "0.710000 3.812968 3.542943           0.270025\n",
      "0.720000 3.718185 3.455007           0.263177\n",
      "0.730000 3.619732 3.363656           0.256076\n",
      "0.740000 3.517707 3.268977           0.248730\n",
      "0.750000 3.412211 3.171065           0.241145\n",
      "0.760000 3.303347 3.070016           0.233331\n",
      "0.770000 3.191223 2.965929           0.225294\n",
      "0.780000 3.075950 2.858907           0.217043\n",
      "0.790000 2.957641 2.749055           0.208586\n",
      "0.800000 2.836413 2.636482           0.199932\n",
      "0.810000 2.712386 2.521297           0.191089\n",
      "0.820000 2.585683 2.403615           0.182068\n",
      "0.830000 2.456427 2.283552           0.172875\n",
      "0.840000 2.324748 2.161226           0.163522\n",
      "0.850000 2.190774 2.036757           0.154017\n",
      "0.860000 2.054638 1.910268           0.144370\n",
      "0.870000 1.916475 1.781884           0.134591\n",
      "0.880000 1.776420 1.651731           0.124689\n",
      "0.890000 1.634612 1.519938           0.114674\n",
      "0.900000 1.491191 1.386634           0.104557\n",
      "0.910000 1.346298 1.251951           0.094347\n",
      "0.920000 1.200077 1.116021           0.084055\n",
      "0.930000 1.052671 0.978979           0.073691\n",
      "0.940000 0.904226 0.840961           0.063266\n",
      "0.950000 0.754889 0.702101           0.052789\n",
      "0.960000 0.604807 0.562537           0.042271\n",
      "0.970000 0.454129 0.422406           0.031723\n",
      "0.980000 0.303002 0.281847           0.021154\n",
      "0.990000 0.151576 0.140999           0.010577\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.78\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.156489 0.145747           0.010743\n",
      "0.020000 0.312824 0.291361           0.021463\n",
      "0.030000 0.468850 0.436699           0.032150\n",
      "0.040000 0.624413 0.581618           0.042795\n",
      "0.050000 0.779360 0.725975           0.053385\n",
      "0.060000 0.933538 0.869626           0.063912\n",
      "0.070000 1.086795 1.012431           0.074364\n",
      "0.080000 1.238979 1.154247           0.084731\n",
      "0.090000 1.389940 1.294936           0.095004\n",
      "0.100000 1.539530 1.434357           0.105173\n",
      "0.110000 1.687600 1.572374           0.115227\n",
      "0.120000 1.834005 1.708849           0.125156\n",
      "0.130000 1.978600 1.843648           0.134952\n",
      "0.140000 2.121242 1.976638           0.144604\n",
      "0.150000 2.261791 2.107687           0.154104\n",
      "0.160000 2.400108 2.236667           0.163441\n",
      "0.170000 2.536056 2.363448           0.172608\n",
      "0.180000 2.669502 2.487906           0.181595\n",
      "0.190000 2.800312 2.609919           0.190394\n",
      "0.200000 2.928360 2.729365           0.198995\n",
      "0.210000 3.053517 2.846126           0.207392\n",
      "0.220000 3.175661 2.960086           0.215575\n",
      "0.230000 3.294671 3.071134           0.223537\n",
      "0.240000 3.410430 3.179159           0.231271\n",
      "0.250000 3.522822 3.284054           0.238768\n",
      "0.260000 3.631739 3.385716           0.246023\n",
      "0.270000 3.737071 3.484044           0.253027\n",
      "0.280000 3.838715 3.578940           0.259775\n",
      "0.290000 3.936571 3.670311           0.266259\n",
      "0.300000 4.030541 3.758067           0.272475\n",
      "0.310000 4.120535 3.842120           0.278415\n",
      "0.320000 4.206461 3.922387           0.284075\n",
      "0.330000 4.288237 3.998788           0.289448\n",
      "0.340000 4.365780 4.071249           0.294531\n",
      "0.350000 4.439015 4.139697           0.299318\n",
      "0.360000 4.507869 4.204064           0.303805\n",
      "0.370000 4.572275 4.264287           0.307988\n",
      "0.380000 4.632168 4.320305           0.311863\n",
      "0.390000 4.687490 4.372063           0.315427\n",
      "0.400000 4.738186 4.419510           0.318675\n",
      "0.410000 4.784205 4.462599           0.321606\n",
      "0.420000 4.825504 4.501287           0.324217\n",
      "0.430000 4.862040 4.535534           0.326506\n",
      "0.440000 4.893778 4.565308           0.328470\n",
      "0.450000 4.920686 4.590579           0.330108\n",
      "0.460000 4.942739 4.611320           0.331418\n",
      "0.470000 4.959913 4.627512           0.332401\n",
      "0.480000 4.972192 4.639138           0.333054\n",
      "0.490000 4.979565 4.646187           0.333378\n",
      "0.500000 4.982023 4.648650           0.333373\n",
      "0.510000 4.979565 4.646526           0.333039\n",
      "0.520000 4.972192 4.639815           0.332377\n",
      "0.530000 4.959913 4.628525           0.331387\n",
      "0.540000 4.942739 4.612667           0.330072\n",
      "0.550000 4.920686 4.592254           0.328432\n",
      "0.560000 4.893778 4.567308           0.326470\n",
      "0.570000 4.862040 4.537853           0.324187\n",
      "0.580000 4.825504 4.503917           0.321587\n",
      "0.590000 4.784205 4.465533           0.318672\n",
      "0.600000 4.738186 4.422740           0.315446\n",
      "0.610000 4.687490 4.375579           0.311911\n",
      "0.620000 4.632168 4.324096           0.308072\n",
      "0.630000 4.572275 4.268341           0.303933\n",
      "0.640000 4.507869 4.208371           0.299499\n",
      "0.650000 4.439015 4.144242           0.294773\n",
      "0.660000 4.365780 4.076019           0.289761\n",
      "0.670000 4.288237 4.003769           0.284468\n",
      "0.680000 4.206461 3.927562           0.278900\n",
      "0.690000 4.120535 3.847473           0.273062\n",
      "0.700000 4.030541 3.763581           0.266961\n",
      "0.710000 3.936571 3.675969           0.260602\n",
      "0.720000 3.838715 3.584723           0.253992\n",
      "0.730000 3.737071 3.489932           0.247139\n",
      "0.740000 3.631739 3.391690           0.240049\n",
      "0.750000 3.522822 3.290094           0.232729\n",
      "0.760000 3.410430 3.185243           0.225186\n",
      "0.770000 3.294671 3.077241           0.217430\n",
      "0.780000 3.175661 2.966195           0.209466\n",
      "0.790000 3.053517 2.852213           0.201304\n",
      "0.800000 2.928360 2.735407           0.192952\n",
      "0.810000 2.800312 2.615894           0.184418\n",
      "0.820000 2.669502 2.493790           0.175711\n",
      "0.830000 2.536056 2.369216           0.166840\n",
      "0.840000 2.400108 2.242295           0.157813\n",
      "0.850000 2.261791 2.113152           0.148640\n",
      "0.860000 2.121242 1.981913           0.139329\n",
      "0.870000 1.978600 1.848709           0.129891\n",
      "0.880000 1.834005 1.713670           0.120335\n",
      "0.890000 1.687600 1.576930           0.110670\n",
      "0.900000 1.539530 1.438624           0.100906\n",
      "0.910000 1.389940 1.298888           0.091053\n",
      "0.920000 1.238979 1.157859           0.081120\n",
      "0.930000 1.086795 1.015677           0.071118\n",
      "0.940000 0.933538 0.872482           0.061056\n",
      "0.950000 0.779360 0.728415           0.050945\n",
      "0.960000 0.624413 0.583619           0.040794\n",
      "0.970000 0.468850 0.438235           0.030614\n",
      "0.980000 0.312824 0.292408           0.020415\n",
      "0.990000 0.156489 0.146282           0.010207\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.79\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.161557 0.151214           0.010343\n",
      "0.020000 0.322955 0.302291           0.020664\n",
      "0.030000 0.484034 0.453080           0.030953\n",
      "0.040000 0.644635 0.603434           0.041201\n",
      "0.050000 0.804600 0.753203           0.051397\n",
      "0.060000 0.963771 0.902240           0.061532\n",
      "0.070000 1.121991 1.050397           0.071595\n",
      "0.080000 1.279104 1.197528           0.081576\n",
      "0.090000 1.434954 1.343488           0.091466\n",
      "0.100000 1.589389 1.488133           0.101256\n",
      "0.110000 1.742254 1.631319           0.110935\n",
      "0.120000 1.893401 1.772906           0.120495\n",
      "0.130000 2.042678 1.912753           0.129926\n",
      "0.140000 2.189940 2.050722           0.139218\n",
      "0.150000 2.335041 2.186677           0.148364\n",
      "0.160000 2.477837 2.320484           0.157353\n",
      "0.170000 2.618188 2.452010           0.166178\n",
      "0.180000 2.755955 2.581125           0.174830\n",
      "0.190000 2.891002 2.707702           0.183301\n",
      "0.200000 3.023197 2.831615           0.191582\n",
      "0.210000 3.152407 2.952742           0.199665\n",
      "0.220000 3.278507 3.070964           0.207543\n",
      "0.230000 3.401371 3.186162           0.215209\n",
      "0.240000 3.520879 3.298225           0.222654\n",
      "0.250000 3.636911 3.407040           0.229872\n",
      "0.260000 3.749355 3.512499           0.236856\n",
      "0.270000 3.858098 3.614500           0.243599\n",
      "0.280000 3.963034 3.712940           0.250095\n",
      "0.290000 4.064059 3.807722           0.256337\n",
      "0.300000 4.161073 3.898753           0.262321\n",
      "0.310000 4.253981 3.985942           0.268039\n",
      "0.320000 4.342690 4.069203           0.273488\n",
      "0.330000 4.427114 4.148453           0.278661\n",
      "0.340000 4.507169 4.223615           0.283554\n",
      "0.350000 4.582776 4.294613           0.288162\n",
      "0.360000 4.653860 4.361378           0.292482\n",
      "0.370000 4.720351 4.423843           0.296508\n",
      "0.380000 4.782184 4.481945           0.300239\n",
      "0.390000 4.839297 4.535629           0.303669\n",
      "0.400000 4.891635 4.584839           0.306796\n",
      "0.410000 4.939145 4.629528           0.309617\n",
      "0.420000 4.981781 4.669650           0.312130\n",
      "0.430000 5.019500 4.705167           0.314333\n",
      "0.440000 5.052266 4.736043           0.316224\n",
      "0.450000 5.080046 4.762246           0.317800\n",
      "0.460000 5.102812 4.783751           0.319061\n",
      "0.470000 5.120543 4.800536           0.320007\n",
      "0.480000 5.133220 4.812585           0.320636\n",
      "0.490000 5.140831 4.819884           0.320947\n",
      "0.500000 5.143369 4.822427           0.320942\n",
      "0.510000 5.140831 4.820211           0.320620\n",
      "0.520000 5.133220 4.813238           0.319982\n",
      "0.530000 5.120543 4.801514           0.319029\n",
      "0.540000 5.102812 4.785050           0.317762\n",
      "0.550000 5.080046 4.763863           0.316183\n",
      "0.560000 5.052266 4.737973           0.314294\n",
      "0.570000 5.019500 4.707405           0.312096\n",
      "0.580000 4.981781 4.672189           0.309592\n",
      "0.590000 4.939145 4.632359           0.306786\n",
      "0.600000 4.891635 4.587956           0.303679\n",
      "0.610000 4.839297 4.539021           0.300276\n",
      "0.620000 4.782184 4.485603           0.296580\n",
      "0.630000 4.720351 4.427755           0.292596\n",
      "0.640000 4.653860 4.365534           0.288326\n",
      "0.650000 4.582776 4.299000           0.283776\n",
      "0.660000 4.507169 4.228218           0.278951\n",
      "0.670000 4.427114 4.153259           0.273855\n",
      "0.680000 4.342690 4.074196           0.268494\n",
      "0.690000 4.253981 3.991107           0.262874\n",
      "0.700000 4.161073 3.904073           0.257000\n",
      "0.710000 4.064059 3.813181           0.250878\n",
      "0.720000 3.963034 3.718519           0.244515\n",
      "0.730000 3.858098 3.620181           0.237917\n",
      "0.740000 3.749355 3.518264           0.231091\n",
      "0.750000 3.636911 3.412868           0.224044\n",
      "0.760000 3.520879 3.304096           0.216783\n",
      "0.770000 3.401371 3.192056           0.209315\n",
      "0.780000 3.278507 3.076858           0.201649\n",
      "0.790000 3.152407 2.958616           0.193791\n",
      "0.800000 3.023197 2.837446           0.185751\n",
      "0.810000 2.891002 2.713467           0.177535\n",
      "0.820000 2.755955 2.586802           0.169153\n",
      "0.830000 2.618188 2.457576           0.160612\n",
      "0.840000 2.477837 2.325915           0.151922\n",
      "0.850000 2.335041 2.191950           0.143091\n",
      "0.860000 2.189940 2.055812           0.134128\n",
      "0.870000 2.042678 1.917636           0.125042\n",
      "0.880000 1.893401 1.777558           0.115843\n",
      "0.890000 1.742254 1.635716           0.106538\n",
      "0.900000 1.589389 1.492250           0.097139\n",
      "0.910000 1.434954 1.347301           0.087653\n",
      "0.920000 1.279104 1.201013           0.078091\n",
      "0.930000 1.121991 1.053529           0.068462\n",
      "0.940000 0.963771 0.904995           0.058776\n",
      "0.950000 0.804600 0.755558           0.049043\n",
      "0.960000 0.644635 0.605364           0.039271\n",
      "0.970000 0.484034 0.454563           0.029471\n",
      "0.980000 0.322955 0.303302           0.019653\n",
      "0.990000 0.161557 0.151731           0.009826\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.8\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.166785 0.156854           0.009931\n",
      "0.020000 0.333405 0.313564           0.019841\n",
      "0.030000 0.499696 0.469975           0.029720\n",
      "0.040000 0.665493 0.625934           0.039560\n",
      "0.050000 0.830635 0.781285           0.049350\n",
      "0.060000 0.994956 0.935876           0.059080\n",
      "0.070000 1.158295 1.089553           0.068742\n",
      "0.080000 1.320492 1.242166           0.078326\n",
      "0.090000 1.481385 1.393563           0.087822\n",
      "0.100000 1.640816 1.543595           0.097221\n",
      "0.110000 1.798628 1.692113           0.106515\n",
      "0.120000 1.954665 1.838971           0.115693\n",
      "0.130000 2.108773 1.984025           0.124748\n",
      "0.140000 2.260800 2.127129           0.133670\n",
      "0.150000 2.410595 2.268144           0.142451\n",
      "0.160000 2.558012 2.406929           0.151082\n",
      "0.170000 2.702904 2.543349           0.159556\n",
      "0.180000 2.845129 2.677266           0.167863\n",
      "0.190000 2.984546 2.808551           0.175995\n",
      "0.200000 3.121018 2.937072           0.183946\n",
      "0.210000 3.254409 3.062702           0.191707\n",
      "0.220000 3.384589 3.185318           0.199271\n",
      "0.230000 3.511429 3.304798           0.206630\n",
      "0.240000 3.634803 3.421024           0.213779\n",
      "0.250000 3.754590 3.533882           0.220709\n",
      "0.260000 3.870672 3.643258           0.227414\n",
      "0.270000 3.982934 3.749046           0.233888\n",
      "0.280000 4.091265 3.851141           0.240124\n",
      "0.290000 4.195559 3.949441           0.246118\n",
      "0.300000 4.295712 4.043850           0.251862\n",
      "0.310000 4.391626 4.134273           0.257353\n",
      "0.320000 4.483206 4.220622           0.262584\n",
      "0.330000 4.570361 4.302811           0.267550\n",
      "0.340000 4.653006 4.380759           0.272248\n",
      "0.350000 4.731060 4.454387           0.276672\n",
      "0.360000 4.804444 4.523625           0.280819\n",
      "0.370000 4.873086 4.588402           0.284685\n",
      "0.380000 4.936920 4.648654           0.288266\n",
      "0.390000 4.995881 4.704322           0.291559\n",
      "0.400000 5.049913 4.755351           0.294561\n",
      "0.410000 5.098960 4.801690           0.297270\n",
      "0.420000 5.142975 4.843293           0.299682\n",
      "0.430000 5.181915 4.880119           0.301797\n",
      "0.440000 5.215741 4.912130           0.303611\n",
      "0.450000 5.244420 4.939295           0.305125\n",
      "0.460000 5.267923 4.961588           0.306335\n",
      "0.470000 5.286227 4.978985           0.307243\n",
      "0.480000 5.299315 4.991469           0.307846\n",
      "0.490000 5.307172 4.999027           0.308145\n",
      "0.500000 5.309792 5.001653           0.308139\n",
      "0.510000 5.307172 4.999342           0.307830\n",
      "0.520000 5.299315 4.992097           0.307217\n",
      "0.530000 5.286227 4.979925           0.306302\n",
      "0.540000 5.267923 4.962838           0.305085\n",
      "0.550000 5.244420 4.940851           0.303569\n",
      "0.560000 5.215741 4.913987           0.301754\n",
      "0.570000 5.181915 4.882271           0.299644\n",
      "0.580000 5.142975 4.845736           0.297240\n",
      "0.590000 5.098960 4.804415           0.294545\n",
      "0.600000 5.049913 4.758350           0.291562\n",
      "0.610000 4.995881 4.707587           0.288295\n",
      "0.620000 4.936920 4.652174           0.284746\n",
      "0.630000 4.873086 4.592167           0.280920\n",
      "0.640000 4.804444 4.527624           0.276820\n",
      "0.650000 4.731060 4.458608           0.272451\n",
      "0.660000 4.653006 4.385188           0.267818\n",
      "0.670000 4.570361 4.307436           0.262926\n",
      "0.680000 4.483206 4.225427           0.257779\n",
      "0.690000 4.391626 4.139244           0.252382\n",
      "0.700000 4.295712 4.048970           0.246742\n",
      "0.710000 4.195559 3.954694           0.240865\n",
      "0.720000 4.091265 3.856510           0.234755\n",
      "0.730000 3.982934 3.754514           0.228420\n",
      "0.740000 3.870672 3.648805           0.221866\n",
      "0.750000 3.754590 3.539490           0.215100\n",
      "0.760000 3.634803 3.426674           0.208129\n",
      "0.770000 3.511429 3.310469           0.200959\n",
      "0.780000 3.384589 3.190990           0.193599\n",
      "0.790000 3.254409 3.068354           0.186055\n",
      "0.800000 3.121018 2.942683           0.178335\n",
      "0.810000 2.984546 2.814099           0.170447\n",
      "0.820000 2.845129 2.682730           0.162399\n",
      "0.830000 2.702904 2.548705           0.154200\n",
      "0.840000 2.558012 2.412156           0.145856\n",
      "0.850000 2.410595 2.273218           0.137378\n",
      "0.860000 2.260800 2.132027           0.128772\n",
      "0.870000 2.108773 1.988724           0.120049\n",
      "0.880000 1.954665 1.843448           0.111217\n",
      "0.890000 1.798628 1.696344           0.102284\n",
      "0.900000 1.640816 1.547557           0.093259\n",
      "0.910000 1.481385 1.397232           0.084153\n",
      "0.920000 1.320492 1.245519           0.074972\n",
      "0.930000 1.158295 1.092567           0.065728\n",
      "0.940000 0.994956 0.938527           0.056429\n",
      "0.950000 0.830635 0.783551           0.047084\n",
      "0.960000 0.665493 0.627791           0.037703\n",
      "0.970000 0.499696 0.471401           0.028294\n",
      "0.980000 0.333405 0.314537           0.018868\n",
      "0.990000 0.166785 0.157351           0.009434\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.81\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.172177 0.162670           0.009507\n",
      "0.020000 0.344183 0.325189           0.018994\n",
      "0.030000 0.515851 0.487398           0.028452\n",
      "0.040000 0.687009 0.649136           0.037872\n",
      "0.050000 0.857489 0.810244           0.047244\n",
      "0.060000 1.027122 0.970563           0.056560\n",
      "0.070000 1.195743 1.129933           0.065810\n",
      "0.080000 1.363183 1.288198           0.074984\n",
      "0.090000 1.529277 1.445202           0.084075\n",
      "0.100000 1.693863 1.600790           0.093074\n",
      "0.110000 1.856777 1.754807           0.101970\n",
      "0.120000 2.017859 1.907101           0.110757\n",
      "0.130000 2.176949 2.057523           0.119426\n",
      "0.140000 2.333890 2.205924           0.127967\n",
      "0.150000 2.488529 2.352156           0.136373\n",
      "0.160000 2.640712 2.496076           0.144636\n",
      "0.170000 2.790288 2.637541           0.152747\n",
      "0.180000 2.937111 2.776412           0.160699\n",
      "0.190000 3.081035 2.912550           0.168485\n",
      "0.200000 3.221919 3.045823           0.176096\n",
      "0.210000 3.359623 3.176097           0.183526\n",
      "0.220000 3.494012 3.303245           0.190767\n",
      "0.230000 3.624952 3.427140           0.197812\n",
      "0.240000 3.752315 3.547660           0.204655\n",
      "0.250000 3.875975 3.664686           0.211289\n",
      "0.260000 3.995810 3.778102           0.217707\n",
      "0.270000 4.111701 3.887796           0.223905\n",
      "0.280000 4.223535 3.993660           0.229875\n",
      "0.290000 4.331200 4.095588           0.235612\n",
      "0.300000 4.434591 4.193480           0.241111\n",
      "0.310000 4.533606 4.287239           0.246367\n",
      "0.320000 4.628146 4.376772           0.251374\n",
      "0.330000 4.718120 4.461991           0.256129\n",
      "0.340000 4.803437 4.542811           0.260626\n",
      "0.350000 4.884013 4.619152           0.264861\n",
      "0.360000 4.959770 4.690939           0.268830\n",
      "0.370000 5.030632 4.758101           0.272531\n",
      "0.380000 5.096529 4.820570           0.275959\n",
      "0.390000 5.157397 4.878286           0.279111\n",
      "0.400000 5.213175 4.931190           0.281984\n",
      "0.410000 5.263808 4.979231           0.284577\n",
      "0.420000 5.309246 5.022360           0.286886\n",
      "0.430000 5.349445 5.060535           0.288910\n",
      "0.440000 5.384364 5.093717           0.290647\n",
      "0.450000 5.413970 5.121875           0.292095\n",
      "0.460000 5.438233 5.144979           0.293254\n",
      "0.470000 5.457129 5.163007           0.294122\n",
      "0.480000 5.470640 5.175940           0.294700\n",
      "0.490000 5.478751 5.183766           0.294985\n",
      "0.500000 5.481456 5.186476           0.294980\n",
      "0.510000 5.478751 5.184068           0.294683\n",
      "0.520000 5.470640 5.176543           0.294096\n",
      "0.530000 5.457129 5.163909           0.293220\n",
      "0.540000 5.438233 5.146178           0.292055\n",
      "0.550000 5.413970 5.123368           0.290603\n",
      "0.560000 5.384364 5.095499           0.288865\n",
      "0.570000 5.349445 5.062600           0.286845\n",
      "0.580000 5.309246 5.024703           0.284543\n",
      "0.590000 5.263808 4.981845           0.281963\n",
      "0.600000 5.213175 4.934067           0.279107\n",
      "0.610000 5.157397 4.881417           0.275979\n",
      "0.620000 5.096529 4.823947           0.272582\n",
      "0.630000 5.030632 4.761713           0.268919\n",
      "0.640000 4.959770 4.694776           0.264994\n",
      "0.650000 4.884013 4.623201           0.260812\n",
      "0.660000 4.803437 4.547060           0.256376\n",
      "0.670000 4.718120 4.466427           0.251692\n",
      "0.680000 4.628146 4.381382           0.246765\n",
      "0.690000 4.533606 4.292007           0.241599\n",
      "0.700000 4.434591 4.198392           0.236200\n",
      "0.710000 4.331200 4.100627           0.230573\n",
      "0.720000 4.223535 3.998810           0.224724\n",
      "0.730000 4.111701 3.893041           0.218660\n",
      "0.740000 3.995810 3.783424           0.212386\n",
      "0.750000 3.875975 3.670066           0.205909\n",
      "0.760000 3.752315 3.553080           0.199235\n",
      "0.770000 3.624952 3.432581           0.192371\n",
      "0.780000 3.494012 3.308686           0.185325\n",
      "0.790000 3.359623 3.181520           0.178103\n",
      "0.800000 3.221919 3.051206           0.170713\n",
      "0.810000 3.081035 2.917873           0.163162\n",
      "0.820000 2.937111 2.781653           0.155458\n",
      "0.830000 2.790288 2.642679           0.147609\n",
      "0.840000 2.640712 2.501090           0.139622\n",
      "0.850000 2.488529 2.357023           0.131506\n",
      "0.860000 2.333890 2.210622           0.123268\n",
      "0.870000 2.176949 2.062031           0.114918\n",
      "0.880000 2.017859 1.911396           0.106463\n",
      "0.890000 1.856777 1.758866           0.097911\n",
      "0.900000 1.693863 1.604590           0.089273\n",
      "0.910000 1.529277 1.448722           0.080555\n",
      "0.920000 1.363183 1.291415           0.071767\n",
      "0.930000 1.195743 1.132824           0.062918\n",
      "0.940000 1.027122 0.973106           0.054016\n",
      "0.950000 0.857489 0.812418           0.045071\n",
      "0.960000 0.687009 0.650918           0.036091\n",
      "0.970000 0.515851 0.488766           0.027084\n",
      "0.980000 0.344183 0.326122           0.018061\n",
      "0.990000 0.172177 0.163147           0.009030\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.8200000000000001\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.177739 0.168666           0.009072\n",
      "0.020000 0.355302 0.337176           0.018126\n",
      "0.030000 0.532515 0.505363           0.027152\n",
      "0.040000 0.709202 0.673061           0.036141\n",
      "0.050000 0.885189 0.840105           0.045084\n",
      "0.060000 1.060303 1.006329           0.053974\n",
      "0.070000 1.234370 1.171570           0.062800\n",
      "0.080000 1.407219 1.335664           0.071555\n",
      "0.090000 1.578680 1.498449           0.080230\n",
      "0.100000 1.748582 1.659765           0.088817\n",
      "0.110000 1.916759 1.819452           0.097307\n",
      "0.120000 2.083044 1.977352           0.105692\n",
      "0.130000 2.247273 2.133310           0.113964\n",
      "0.140000 2.409285 2.287171           0.122114\n",
      "0.150000 2.568919 2.438783           0.130136\n",
      "0.160000 2.726018 2.587997           0.138021\n",
      "0.170000 2.880426 2.734665           0.145761\n",
      "0.180000 3.031992 2.878643           0.153349\n",
      "0.190000 3.180566 3.019787           0.160778\n",
      "0.200000 3.326001 3.157959           0.168041\n",
      "0.210000 3.468153 3.293022           0.175131\n",
      "0.220000 3.606883 3.424843           0.182040\n",
      "0.230000 3.742053 3.553290           0.188763\n",
      "0.240000 3.873531 3.678238           0.195293\n",
      "0.250000 4.001185 3.799562           0.201623\n",
      "0.260000 4.124891 3.917143           0.207748\n",
      "0.270000 4.244526 4.030865           0.213661\n",
      "0.280000 4.359973 4.140614           0.219358\n",
      "0.290000 4.471116 4.246283           0.224833\n",
      "0.300000 4.577847 4.347767           0.230080\n",
      "0.310000 4.680061 4.444965           0.235095\n",
      "0.320000 4.777655 4.537782           0.239873\n",
      "0.330000 4.870535 4.626125           0.244410\n",
      "0.340000 4.958608 4.709907           0.248701\n",
      "0.350000 5.041787 4.789046           0.252742\n",
      "0.360000 5.119991 4.863462           0.256529\n",
      "0.370000 5.193142 4.933082           0.260060\n",
      "0.380000 5.261168 4.997838           0.263331\n",
      "0.390000 5.324002 5.057664           0.266339\n",
      "0.400000 5.381582 5.112502           0.269080\n",
      "0.410000 5.433851 5.162297           0.271554\n",
      "0.420000 5.480757 5.207000           0.273757\n",
      "0.430000 5.522255 5.246566           0.275688\n",
      "0.440000 5.558302 5.280957           0.277345\n",
      "0.450000 5.588864 5.310137           0.278727\n",
      "0.460000 5.613911 5.334079           0.279833\n",
      "0.470000 5.633418 5.352757           0.280661\n",
      "0.480000 5.647365 5.366153           0.281211\n",
      "0.490000 5.655738 5.374254           0.281484\n",
      "0.500000 5.658530 5.377052           0.281478\n",
      "0.510000 5.655738 5.374543           0.281195\n",
      "0.520000 5.647365 5.366730           0.280635\n",
      "0.530000 5.633418 5.353620           0.279798\n",
      "0.540000 5.613911 5.335225           0.278686\n",
      "0.550000 5.588864 5.311564           0.277300\n",
      "0.560000 5.558302 5.282660           0.275642\n",
      "0.570000 5.522255 5.248541           0.273714\n",
      "0.580000 5.480757 5.209240           0.271517\n",
      "0.590000 5.433851 5.164796           0.269055\n",
      "0.600000 5.381582 5.115253           0.266330\n",
      "0.610000 5.324002 5.060658           0.263344\n",
      "0.620000 5.261168 5.001066           0.260102\n",
      "0.630000 5.193142 4.936536           0.256606\n",
      "0.640000 5.119991 4.867130           0.252861\n",
      "0.650000 5.041787 4.792917           0.248870\n",
      "0.660000 4.958608 4.713970           0.244638\n",
      "0.670000 4.870535 4.630367           0.240168\n",
      "0.680000 4.777655 4.542189           0.235466\n",
      "0.690000 4.680061 4.449525           0.230536\n",
      "0.700000 4.577847 4.352463           0.225384\n",
      "0.710000 4.471116 4.251102           0.220014\n",
      "0.720000 4.359973 4.145539           0.214433\n",
      "0.730000 4.244526 4.035880           0.208646\n",
      "0.740000 4.124891 3.922232           0.202660\n",
      "0.750000 4.001185 3.804706           0.196479\n",
      "0.760000 3.873531 3.683420           0.190111\n",
      "0.770000 3.742053 3.558492           0.183561\n",
      "0.780000 3.606883 3.430045           0.176838\n",
      "0.790000 3.468153 3.298207           0.169946\n",
      "0.800000 3.326001 3.163106           0.162894\n",
      "0.810000 3.180566 3.024877           0.155689\n",
      "0.820000 3.031992 2.883654           0.148338\n",
      "0.830000 2.880426 2.739578           0.140848\n",
      "0.840000 2.726018 2.592791           0.133227\n",
      "0.850000 2.568919 2.443437           0.125482\n",
      "0.860000 2.409285 2.291663           0.117622\n",
      "0.870000 2.247273 2.137620           0.109654\n",
      "0.880000 2.083044 1.981458           0.101586\n",
      "0.890000 1.916759 1.823333           0.093426\n",
      "0.900000 1.748582 1.663399           0.085183\n",
      "0.910000 1.578680 1.501815           0.076865\n",
      "0.920000 1.407219 1.338740           0.068479\n",
      "0.930000 1.234370 1.174335           0.060036\n",
      "0.940000 1.060303 1.008761           0.051542\n",
      "0.950000 0.885189 0.842183           0.043006\n",
      "0.960000 0.709202 0.674765           0.034437\n",
      "0.970000 0.532515 0.506671           0.025843\n",
      "0.980000 0.355302 0.338068           0.017234\n",
      "0.990000 0.177739 0.169122           0.008616\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.8300000000000001\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.183476 0.174849           0.008627\n",
      "0.020000 0.366771 0.349535           0.017236\n",
      "0.030000 0.549705 0.523886           0.025819\n",
      "0.040000 0.732095 0.697728           0.034367\n",
      "0.050000 0.913763 0.870892           0.042871\n",
      "0.060000 1.094530 1.043205           0.051324\n",
      "0.070000 1.274216 1.214498           0.059718\n",
      "0.080000 1.452645 1.384602           0.068043\n",
      "0.090000 1.629640 1.553348           0.076292\n",
      "0.100000 1.805027 1.720570           0.084457\n",
      "0.110000 1.978632 1.886102           0.092530\n",
      "0.120000 2.150285 2.049782           0.100504\n",
      "0.130000 2.319816 2.211447           0.108369\n",
      "0.140000 2.487058 2.370938           0.116119\n",
      "0.150000 2.651845 2.528098           0.123747\n",
      "0.160000 2.814015 2.682770           0.131245\n",
      "0.170000 2.973408 2.834803           0.138605\n",
      "0.180000 3.129866 2.984046           0.145820\n",
      "0.190000 3.283236 3.130351           0.152885\n",
      "0.200000 3.433365 3.273574           0.159791\n",
      "0.210000 3.580106 3.413574           0.166532\n",
      "0.220000 3.723315 3.550212           0.173102\n",
      "0.230000 3.862848 3.683354           0.179495\n",
      "0.240000 3.998570 3.812866           0.185703\n",
      "0.250000 4.130345 3.938622           0.191723\n",
      "0.260000 4.258044 4.060498           0.197547\n",
      "0.270000 4.381541 4.178371           0.203170\n",
      "0.280000 4.500714 4.292128           0.208587\n",
      "0.290000 4.615445 4.401653           0.213792\n",
      "0.300000 4.725622 4.506840           0.218782\n",
      "0.310000 4.831135 4.607585           0.223550\n",
      "0.320000 4.931880 4.703787           0.228093\n",
      "0.330000 5.027758 4.795351           0.232407\n",
      "0.340000 5.118674 4.882187           0.236487\n",
      "0.350000 5.204538 4.964209           0.240329\n",
      "0.360000 5.285267 5.041336           0.243930\n",
      "0.370000 5.360779 5.113491           0.247288\n",
      "0.380000 5.431001 5.180604           0.250397\n",
      "0.390000 5.495863 5.242606           0.253257\n",
      "0.400000 5.555302 5.299438           0.255864\n",
      "0.410000 5.609258 5.351042           0.258216\n",
      "0.420000 5.657678 5.397367           0.260311\n",
      "0.430000 5.700515 5.438368           0.262147\n",
      "0.440000 5.737726 5.474004           0.263722\n",
      "0.450000 5.769275 5.504239           0.265036\n",
      "0.460000 5.795130 5.529044           0.266086\n",
      "0.470000 5.815266 5.548393           0.266874\n",
      "0.480000 5.829664 5.562267           0.267397\n",
      "0.490000 5.838308 5.570652           0.267656\n",
      "0.500000 5.841190 5.573540           0.267650\n",
      "0.510000 5.838308 5.570927           0.267381\n",
      "0.520000 5.829664 5.562816           0.266847\n",
      "0.530000 5.815266 5.549215           0.266052\n",
      "0.540000 5.795130 5.530136           0.264994\n",
      "0.550000 5.769275 5.505599           0.263676\n",
      "0.560000 5.737726 5.475627           0.262099\n",
      "0.570000 5.700515 5.440250           0.260265\n",
      "0.580000 5.657678 5.399502           0.258176\n",
      "0.590000 5.609258 5.353423           0.255835\n",
      "0.600000 5.555302 5.302058           0.253243\n",
      "0.610000 5.495863 5.245459           0.250404\n",
      "0.620000 5.431001 5.183680           0.247321\n",
      "0.630000 5.360779 5.116782           0.243997\n",
      "0.640000 5.285267 5.044831           0.240436\n",
      "0.650000 5.204538 4.967898           0.236641\n",
      "0.660000 5.118674 4.886058           0.232616\n",
      "0.670000 5.027758 4.799392           0.228365\n",
      "0.680000 4.931880 4.707986           0.223894\n",
      "0.690000 4.831135 4.611928           0.219206\n",
      "0.700000 4.725622 4.511315           0.214307\n",
      "0.710000 4.615445 4.406244           0.209202\n",
      "0.720000 4.500714 4.296820           0.203895\n",
      "0.730000 4.381541 4.183149           0.198392\n",
      "0.740000 4.258044 4.065345           0.192699\n",
      "0.750000 4.130345 3.943523           0.186822\n",
      "0.760000 3.998570 3.817803           0.180766\n",
      "0.770000 3.862848 3.688309           0.174539\n",
      "0.780000 3.723315 3.555169           0.168145\n",
      "0.790000 3.580106 3.418514           0.161593\n",
      "0.800000 3.433365 3.278478           0.154887\n",
      "0.810000 3.283236 3.135199           0.148036\n",
      "0.820000 3.129866 2.988820           0.141046\n",
      "0.830000 2.973408 2.839483           0.133924\n",
      "0.840000 2.814015 2.687337           0.126677\n",
      "0.850000 2.651845 2.532531           0.119313\n",
      "0.860000 2.487058 2.375218           0.111839\n",
      "0.870000 2.319816 2.215553           0.104263\n",
      "0.880000 2.150285 2.053694           0.096591\n",
      "0.890000 1.978632 1.889800           0.088833\n",
      "0.900000 1.805027 1.724032           0.080995\n",
      "0.910000 1.629640 1.556554           0.073086\n",
      "0.920000 1.452645 1.387532           0.065113\n",
      "0.930000 1.274216 1.217132           0.057084\n",
      "0.940000 1.094530 1.045522           0.049007\n",
      "0.950000 0.913763 0.872872           0.040891\n",
      "0.960000 0.732095 0.699351           0.032744\n",
      "0.970000 0.549705 0.525132           0.024573\n",
      "0.980000 0.366771 0.350385           0.016386\n",
      "0.990000 0.183476 0.175284           0.008193\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.84\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.189395 0.181223           0.008172\n",
      "0.020000 0.378603 0.362276           0.016327\n",
      "0.030000 0.567437 0.542981           0.024456\n",
      "0.040000 0.755711 0.723158           0.032553\n",
      "0.050000 0.943240 0.902631           0.040608\n",
      "0.060000 1.129837 1.081222           0.048615\n",
      "0.070000 1.315320 1.258754           0.056565\n",
      "0.080000 1.499504 1.435053           0.064451\n",
      "0.090000 1.682209 1.609944           0.072265\n",
      "0.100000 1.863253 1.783254           0.079999\n",
      "0.110000 2.042459 1.954813           0.087646\n",
      "0.120000 2.219649 2.124451           0.095198\n",
      "0.130000 2.394649 2.292001           0.102648\n",
      "0.140000 2.567285 2.457296           0.109989\n",
      "0.150000 2.737388 2.620174           0.117214\n",
      "0.160000 2.904789 2.780473           0.124316\n",
      "0.170000 3.069324 2.938036           0.131287\n",
      "0.180000 3.230829 3.092707           0.138122\n",
      "0.190000 3.389146 3.244333           0.144813\n",
      "0.200000 3.544119 3.392764           0.151354\n",
      "0.210000 3.695593 3.537854           0.157740\n",
      "0.220000 3.843421 3.679459           0.163963\n",
      "0.230000 3.987456 3.817438           0.170017\n",
      "0.240000 4.127555 3.951657           0.175898\n",
      "0.250000 4.263582 4.081982           0.181599\n",
      "0.260000 4.395400 4.208284           0.187116\n",
      "0.270000 4.522881 4.330439           0.192442\n",
      "0.280000 4.645898 4.448326           0.197572\n",
      "0.290000 4.764330 4.561827           0.202503\n",
      "0.300000 4.878061 4.670832           0.207229\n",
      "0.310000 4.986977 4.775232           0.211745\n",
      "0.320000 5.090972 4.874924           0.216048\n",
      "0.330000 5.189943 4.969809           0.220134\n",
      "0.340000 5.283792 5.059794           0.223998\n",
      "0.350000 5.372426 5.144789           0.227637\n",
      "0.360000 5.455759 5.224711           0.231048\n",
      "0.370000 5.533707 5.299479           0.234228\n",
      "0.380000 5.606194 5.369021           0.237173\n",
      "0.390000 5.673149 5.433267           0.239882\n",
      "0.400000 5.734504 5.492154           0.242351\n",
      "0.410000 5.790201 5.545623           0.244578\n",
      "0.420000 5.840183 5.593621           0.246562\n",
      "0.430000 5.884402 5.636102           0.248301\n",
      "0.440000 5.922814 5.673021           0.249793\n",
      "0.450000 5.955380 5.704344           0.251037\n",
      "0.460000 5.982070 5.730038           0.252032\n",
      "0.470000 6.002855 5.750078           0.252777\n",
      "0.480000 6.017717 5.764444           0.253272\n",
      "0.490000 6.026640 5.773122           0.253517\n",
      "0.500000 6.029615 5.776103           0.253512\n",
      "0.510000 6.026640 5.773383           0.253256\n",
      "0.520000 6.017717 5.764966           0.252751\n",
      "0.530000 6.002855 5.750858           0.251997\n",
      "0.540000 5.982070 5.731074           0.250995\n",
      "0.550000 5.955380 5.705634           0.249746\n",
      "0.560000 5.922814 5.674561           0.248253\n",
      "0.570000 5.884402 5.637887           0.246515\n",
      "0.580000 5.840183 5.595647           0.244537\n",
      "0.590000 5.790201 5.547882           0.242319\n",
      "0.600000 5.734504 5.494641           0.239864\n",
      "0.610000 5.673149 5.435974           0.237175\n",
      "0.620000 5.606194 5.371940           0.234254\n",
      "0.630000 5.533707 5.302601           0.231105\n",
      "0.640000 5.455759 5.228027           0.227732\n",
      "0.650000 5.372426 5.148289           0.224137\n",
      "0.660000 5.283792 5.063467           0.220325\n",
      "0.670000 5.189943 4.973644           0.216299\n",
      "0.680000 5.090972 4.878908           0.212064\n",
      "0.690000 4.986977 4.779354           0.207623\n",
      "0.700000 4.878061 4.675078           0.202983\n",
      "0.710000 4.764330 4.566184           0.198147\n",
      "0.720000 4.645898 4.452778           0.193120\n",
      "0.730000 4.522881 4.334973           0.187908\n",
      "0.740000 4.395400 4.212884           0.182516\n",
      "0.750000 4.263582 4.086632           0.176949\n",
      "0.760000 4.127555 3.956342           0.171214\n",
      "0.770000 3.987456 3.822141           0.165315\n",
      "0.780000 3.843421 3.684162           0.159259\n",
      "0.790000 3.695593 3.542541           0.153053\n",
      "0.800000 3.544119 3.397417           0.146702\n",
      "0.810000 3.389146 3.248934           0.140212\n",
      "0.820000 3.230829 3.097238           0.133592\n",
      "0.830000 3.069324 2.942478           0.126846\n",
      "0.840000 2.904789 2.784807           0.119982\n",
      "0.850000 2.737388 2.624381           0.113007\n",
      "0.860000 2.567285 2.461357           0.105928\n",
      "0.870000 2.394649 2.295897           0.098752\n",
      "0.880000 2.219649 2.128163           0.091486\n",
      "0.890000 2.042459 1.958322           0.084137\n",
      "0.900000 1.863253 1.786540           0.076714\n",
      "0.910000 1.682209 1.612987           0.069222\n",
      "0.920000 1.499504 1.437834           0.061671\n",
      "0.930000 1.315320 1.261253           0.054066\n",
      "0.940000 1.129837 1.083420           0.046417\n",
      "0.950000 0.943240 0.904510           0.038730\n",
      "0.960000 0.755711 0.724698           0.031013\n",
      "0.970000 0.567437 0.544163           0.023274\n",
      "0.980000 0.378603 0.363083           0.015520\n",
      "0.990000 0.189395 0.181635           0.007760\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.85\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.195500 0.187793           0.007707\n",
      "0.020000 0.390808 0.375410           0.015398\n",
      "0.030000 0.585729 0.562664           0.023065\n",
      "0.040000 0.780073 0.749372           0.030701\n",
      "0.050000 0.973647 0.935348           0.038298\n",
      "0.060000 1.166260 1.120410           0.045850\n",
      "0.070000 1.357722 1.304374           0.053347\n",
      "0.080000 1.547844 1.487059           0.060785\n",
      "0.090000 1.736438 1.668285           0.068154\n",
      "0.100000 1.923319 1.847872           0.075448\n",
      "0.110000 2.108302 2.025643           0.082659\n",
      "0.120000 2.291204 2.201422           0.089782\n",
      "0.130000 2.471845 2.375037           0.096808\n",
      "0.140000 2.650047 2.546315           0.103731\n",
      "0.150000 2.825633 2.715088           0.110545\n",
      "0.160000 2.998431 2.881188           0.117242\n",
      "0.170000 3.168269 3.044452           0.123817\n",
      "0.180000 3.334981 3.204719           0.130263\n",
      "0.190000 3.498402 3.361829           0.136573\n",
      "0.200000 3.658370 3.515628           0.142742\n",
      "0.210000 3.814728 3.665964           0.148764\n",
      "0.220000 3.967321 3.812689           0.154632\n",
      "0.230000 4.115999 3.955657           0.160343\n",
      "0.240000 4.260615 4.094727           0.165889\n",
      "0.250000 4.401026 4.229761           0.171265\n",
      "0.260000 4.537094 4.360627           0.176467\n",
      "0.270000 4.668685 4.487195           0.181490\n",
      "0.280000 4.795668 4.609339           0.186329\n",
      "0.290000 4.917918 4.726940           0.190978\n",
      "0.300000 5.035315 4.839880           0.195435\n",
      "0.310000 5.147742 4.948048           0.199694\n",
      "0.320000 5.255090 5.051337           0.203752\n",
      "0.330000 5.357251 5.149646           0.207605\n",
      "0.340000 5.454125 5.242876           0.211249\n",
      "0.350000 5.545617 5.330936           0.214681\n",
      "0.360000 5.631636 5.413738           0.217898\n",
      "0.370000 5.712097 5.491201           0.220896\n",
      "0.380000 5.786921 5.563247           0.223674\n",
      "0.390000 5.856034 5.629806           0.226228\n",
      "0.400000 5.919367 5.690811           0.228556\n",
      "0.410000 5.976860 5.746203           0.230657\n",
      "0.420000 6.028453 5.795926           0.232527\n",
      "0.430000 6.074097 5.839931           0.234167\n",
      "0.440000 6.113747 5.878174           0.235574\n",
      "0.450000 6.147364 5.910617           0.236747\n",
      "0.460000 6.174913 5.937228           0.237685\n",
      "0.470000 6.196369 5.957981           0.238388\n",
      "0.480000 6.211710 5.972855           0.238855\n",
      "0.490000 6.220920 5.981835           0.239085\n",
      "0.500000 6.223991 5.984911           0.239080\n",
      "0.510000 6.220920 5.982081           0.238839\n",
      "0.520000 6.211710 5.973348           0.238362\n",
      "0.530000 6.196369 5.958718           0.237651\n",
      "0.540000 6.174913 5.938208           0.236706\n",
      "0.550000 6.147364 5.911836           0.235528\n",
      "0.560000 6.113747 5.879628           0.234119\n",
      "0.570000 6.074097 5.841617           0.232480\n",
      "0.580000 6.028453 5.797839           0.230614\n",
      "0.590000 5.976860 5.748337           0.228522\n",
      "0.600000 5.919367 5.693161           0.226207\n",
      "0.610000 5.856034 5.632363           0.223671\n",
      "0.620000 5.786921 5.566005           0.220916\n",
      "0.630000 5.712097 5.494150           0.217947\n",
      "0.640000 5.631636 5.416871           0.214765\n",
      "0.650000 5.545617 5.334242           0.211375\n",
      "0.660000 5.454125 5.246346           0.207779\n",
      "0.670000 5.357251 5.153268           0.203982\n",
      "0.680000 5.255090 5.055101           0.199988\n",
      "0.690000 5.147742 4.951942           0.195801\n",
      "0.700000 5.035315 4.843891           0.191424\n",
      "0.710000 4.917918 4.731055           0.186863\n",
      "0.720000 4.795668 4.613545           0.182123\n",
      "0.730000 4.668685 4.491477           0.177207\n",
      "0.740000 4.537094 4.364972           0.172122\n",
      "0.750000 4.401026 4.234154           0.166872\n",
      "0.760000 4.260615 4.099152           0.161463\n",
      "0.770000 4.115999 3.960099           0.155900\n",
      "0.780000 3.967321 3.817132           0.150189\n",
      "0.790000 3.814728 3.670392           0.144336\n",
      "0.800000 3.658370 3.520024           0.138347\n",
      "0.810000 3.498402 3.366175           0.132227\n",
      "0.820000 3.334981 3.208998           0.125983\n",
      "0.830000 3.168269 3.048648           0.119621\n",
      "0.840000 2.998431 2.885282           0.113148\n",
      "0.850000 2.825633 2.719062           0.106571\n",
      "0.860000 2.650047 2.550152           0.099895\n",
      "0.870000 2.471845 2.378718           0.093127\n",
      "0.880000 2.291204 2.204929           0.086275\n",
      "0.890000 2.108302 2.028957           0.079345\n",
      "0.900000 1.923319 1.850975           0.072344\n",
      "0.910000 1.736438 1.671159           0.065279\n",
      "0.920000 1.547844 1.489686           0.058158\n",
      "0.930000 1.357722 1.306735           0.050986\n",
      "0.940000 1.166260 1.122487           0.043773\n",
      "0.950000 0.973647 0.937123           0.036523\n",
      "0.960000 0.780073 0.750827           0.029246\n",
      "0.970000 0.585729 0.563782           0.021948\n",
      "0.980000 0.390808 0.376172           0.014636\n",
      "0.990000 0.195500 0.188183           0.007318\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.86\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.201799 0.194566           0.007233\n",
      "0.020000 0.403398 0.388947           0.014451\n",
      "0.030000 0.604600 0.582953           0.021647\n",
      "0.040000 0.805205 0.776391           0.028813\n",
      "0.050000 1.005015 0.969071           0.035944\n",
      "0.060000 1.203833 1.160803           0.043030\n",
      "0.070000 1.401464 1.351396           0.050067\n",
      "0.080000 1.597711 1.540664           0.057047\n",
      "0.090000 1.792381 1.728418           0.063963\n",
      "0.100000 1.985283 1.914475           0.070808\n",
      "0.110000 2.176226 2.098649           0.077577\n",
      "0.120000 2.365020 2.280759           0.084261\n",
      "0.130000 2.551481 2.460626           0.090855\n",
      "0.140000 2.735424 2.638071           0.097353\n",
      "0.150000 2.916667 2.812920           0.103747\n",
      "0.160000 3.095032 2.984999           0.110033\n",
      "0.170000 3.270342 3.154139           0.116203\n",
      "0.180000 3.442425 3.320173           0.122252\n",
      "0.190000 3.611111 3.482937           0.128174\n",
      "0.200000 3.776233 3.642269           0.133964\n",
      "0.210000 3.937628 3.798013           0.139615\n",
      "0.220000 4.095137 3.950015           0.145123\n",
      "0.230000 4.248605 4.098124           0.150482\n",
      "0.240000 4.397880 4.242194           0.155686\n",
      "0.250000 4.542815 4.382083           0.160732\n",
      "0.260000 4.683267 4.517653           0.165614\n",
      "0.270000 4.819097 4.648769           0.170328\n",
      "0.280000 4.950171 4.775302           0.174869\n",
      "0.290000 5.076360 4.897127           0.179232\n",
      "0.300000 5.197539 5.014124           0.183415\n",
      "0.310000 5.313588 5.126176           0.187412\n",
      "0.320000 5.424394 5.233174           0.191220\n",
      "0.330000 5.529847 5.335011           0.194836\n",
      "0.340000 5.629842 5.431586           0.198256\n",
      "0.350000 5.724281 5.522805           0.201476\n",
      "0.360000 5.813071 5.608576           0.204495\n",
      "0.370000 5.896125 5.688816           0.207309\n",
      "0.380000 5.973359 5.763444           0.209915\n",
      "0.390000 6.044699 5.832387           0.212312\n",
      "0.400000 6.110073 5.895576           0.214497\n",
      "0.410000 6.169417 5.952949           0.216468\n",
      "0.420000 6.222673 6.004450           0.218224\n",
      "0.430000 6.269788 6.050026           0.219762\n",
      "0.440000 6.310715 6.089633           0.221082\n",
      "0.450000 6.345415 6.123232           0.222183\n",
      "0.460000 6.373852 6.150789           0.223063\n",
      "0.470000 6.395999 6.172276           0.223723\n",
      "0.480000 6.411834 6.187673           0.224161\n",
      "0.490000 6.421341 6.196964           0.224377\n",
      "0.500000 6.424511 6.200139           0.224372\n",
      "0.510000 6.421341 6.197196           0.224145\n",
      "0.520000 6.411834 6.188136           0.223698\n",
      "0.530000 6.395999 6.172969           0.223030\n",
      "0.540000 6.373852 6.151709           0.222143\n",
      "0.550000 6.345415 6.124377           0.221037\n",
      "0.560000 6.310715 6.091001           0.219715\n",
      "0.570000 6.269788 6.051611           0.218177\n",
      "0.580000 6.222673 6.006248           0.216425\n",
      "0.590000 6.169417 5.954956           0.214462\n",
      "0.600000 6.110073 5.897784           0.212289\n",
      "0.610000 6.044699 5.834791           0.209908\n",
      "0.620000 5.973359 5.766036           0.207323\n",
      "0.630000 5.896125 5.691588           0.204536\n",
      "0.640000 5.813071 5.611521           0.201550\n",
      "0.650000 5.724281 5.525913           0.198368\n",
      "0.660000 5.629842 5.434848           0.194994\n",
      "0.670000 5.529847 5.338416           0.191431\n",
      "0.680000 5.424394 5.236712           0.187682\n",
      "0.690000 5.313588 5.129836           0.183752\n",
      "0.700000 5.197539 5.017894           0.179645\n",
      "0.710000 5.076360 4.900995           0.175364\n",
      "0.720000 4.950171 4.779255           0.170915\n",
      "0.730000 4.819097 4.652795           0.166302\n",
      "0.740000 4.683267 4.521737           0.161530\n",
      "0.750000 4.542815 4.386212           0.156603\n",
      "0.760000 4.397880 4.246354           0.151527\n",
      "0.770000 4.248605 4.102299           0.146306\n",
      "0.780000 4.095137 3.954191           0.140946\n",
      "0.790000 3.937628 3.802175           0.135453\n",
      "0.800000 3.776233 3.646401           0.129832\n",
      "0.810000 3.611111 3.487022           0.124089\n",
      "0.820000 3.442425 3.324196           0.118229\n",
      "0.830000 3.270342 3.158083           0.112259\n",
      "0.840000 3.095032 2.988847           0.106184\n",
      "0.850000 2.916667 2.816656           0.100011\n",
      "0.860000 2.735424 2.641677           0.093746\n",
      "0.870000 2.551481 2.464086           0.087395\n",
      "0.880000 2.365020 2.284056           0.080965\n",
      "0.890000 2.176226 2.101764           0.074461\n",
      "0.900000 1.985283 1.917392           0.067891\n",
      "0.910000 1.792381 1.731120           0.061261\n",
      "0.920000 1.597711 1.543133           0.054578\n",
      "0.930000 1.401464 1.353616           0.047848\n",
      "0.940000 1.203833 1.162755           0.041078\n",
      "0.950000 1.005015 0.970740           0.034275\n",
      "0.960000 0.805205 0.777759           0.027446\n",
      "0.970000 0.604600 0.584003           0.020597\n",
      "0.980000 0.403398 0.389663           0.013735\n",
      "0.990000 0.201799 0.194932           0.006867\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.87\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.208296 0.201546           0.006751\n",
      "0.020000 0.416387 0.402900           0.013488\n",
      "0.030000 0.624067 0.603864           0.020204\n",
      "0.040000 0.831131 0.804239           0.026892\n",
      "0.050000 1.037375 1.003828           0.033547\n",
      "0.060000 1.242595 1.202434           0.040161\n",
      "0.070000 1.446589 1.399860           0.046729\n",
      "0.080000 1.649155 1.595912           0.053243\n",
      "0.090000 1.850094 1.790396           0.059698\n",
      "0.100000 2.049207 1.983120           0.066087\n",
      "0.110000 2.246297 2.173893           0.072404\n",
      "0.120000 2.441171 2.362528           0.078643\n",
      "0.130000 2.633635 2.548838           0.084797\n",
      "0.140000 2.823501 2.732640           0.090861\n",
      "0.150000 3.010580 2.913751           0.096829\n",
      "0.160000 3.194688 3.091992           0.102696\n",
      "0.170000 3.375643 3.267189           0.108454\n",
      "0.180000 3.553267 3.439167           0.114100\n",
      "0.190000 3.727384 3.607757           0.119627\n",
      "0.200000 3.897823 3.772792           0.125030\n",
      "0.210000 4.064415 3.934110           0.130305\n",
      "0.220000 4.226996 4.091551           0.135445\n",
      "0.230000 4.385405 4.244959           0.140447\n",
      "0.240000 4.539487 4.394182           0.145304\n",
      "0.250000 4.689088 4.539075           0.150013\n",
      "0.260000 4.834062 4.679492           0.154570\n",
      "0.270000 4.974266 4.815297           0.158969\n",
      "0.280000 5.109560 4.946353           0.163207\n",
      "0.290000 5.239812 5.072533           0.167279\n",
      "0.300000 5.364893 5.193710           0.171183\n",
      "0.310000 5.484679 5.309766           0.174913\n",
      "0.320000 5.599053 5.420586           0.178467\n",
      "0.330000 5.707901 5.526059           0.181841\n",
      "0.340000 5.811116 5.626083           0.185033\n",
      "0.350000 5.908596 5.720557           0.188039\n",
      "0.360000 6.000245 5.809389           0.190856\n",
      "0.370000 6.085972 5.892490           0.193482\n",
      "0.380000 6.165694 5.969779           0.195915\n",
      "0.390000 6.239330 6.041179           0.198151\n",
      "0.400000 6.306810 6.106619           0.200190\n",
      "0.410000 6.368065 6.166035           0.202030\n",
      "0.420000 6.423035 6.219367           0.203668\n",
      "0.430000 6.471667 6.266563           0.205104\n",
      "0.440000 6.513912 6.307577           0.206336\n",
      "0.450000 6.549729 6.342366           0.207363\n",
      "0.460000 6.579082 6.370898           0.208184\n",
      "0.470000 6.601942 6.393142           0.208799\n",
      "0.480000 6.618287 6.409079           0.209208\n",
      "0.490000 6.628100 6.418690           0.209410\n",
      "0.500000 6.631372 6.421967           0.209405\n",
      "0.510000 6.628100 6.418907           0.209193\n",
      "0.520000 6.618287 6.409511           0.208775\n",
      "0.530000 6.601942 6.393790           0.208152\n",
      "0.540000 6.579082 6.371758           0.207324\n",
      "0.550000 6.549729 6.343437           0.206292\n",
      "0.560000 6.513912 6.308855           0.205058\n",
      "0.570000 6.471667 6.268045           0.203622\n",
      "0.580000 6.423035 6.221048           0.201987\n",
      "0.590000 6.368065 6.167910           0.200154\n",
      "0.600000 6.306810 6.108683           0.198126\n",
      "0.610000 6.239330 6.043426           0.195905\n",
      "0.620000 6.165694 5.972202           0.193492\n",
      "0.630000 6.085972 5.895082           0.190891\n",
      "0.640000 6.000245 5.812141           0.188104\n",
      "0.650000 5.908596 5.723462           0.185134\n",
      "0.660000 5.811116 5.629131           0.181985\n",
      "0.670000 5.707901 5.529242           0.178659\n",
      "0.680000 5.599053 5.423893           0.175160\n",
      "0.690000 5.484679 5.313187           0.171492\n",
      "0.700000 5.364893 5.197234           0.167659\n",
      "0.710000 5.239812 5.076148           0.163664\n",
      "0.720000 5.109560 4.950048           0.159512\n",
      "0.730000 4.974266 4.819059           0.155206\n",
      "0.740000 4.834062 4.683310           0.150752\n",
      "0.750000 4.689088 4.542934           0.146154\n",
      "0.760000 4.539487 4.398071           0.141416\n",
      "0.770000 4.385405 4.248861           0.136544\n",
      "0.780000 4.226996 4.095454           0.131542\n",
      "0.790000 4.064415 3.938000           0.126415\n",
      "0.800000 3.897823 3.776654           0.121169\n",
      "0.810000 3.727384 3.611575           0.115809\n",
      "0.820000 3.553267 3.442927           0.110340\n",
      "0.830000 3.375643 3.270875           0.104768\n",
      "0.840000 3.194688 3.095589           0.099099\n",
      "0.850000 3.010580 2.917242           0.093338\n",
      "0.860000 2.823501 2.736011           0.087490\n",
      "0.870000 2.633635 2.552072           0.081563\n",
      "0.880000 2.441171 2.365609           0.075562\n",
      "0.890000 2.246297 2.176805           0.069492\n",
      "0.900000 2.049207 1.985846           0.063361\n",
      "0.910000 1.850094 1.792921           0.057173\n",
      "0.920000 1.649155 1.598220           0.050936\n",
      "0.930000 1.446589 1.401934           0.044655\n",
      "0.940000 1.242595 1.204258           0.038337\n",
      "0.950000 1.037375 1.005387           0.031988\n",
      "0.960000 0.831131 0.805517           0.025614\n",
      "0.970000 0.624067 0.604845           0.019222\n",
      "0.980000 0.416387 0.403569           0.012818\n",
      "0.990000 0.208296 0.201888           0.006409\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.88\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.215000 0.208739           0.006261\n",
      "0.020000 0.429787 0.417279           0.012509\n",
      "0.030000 0.644151 0.625414           0.018737\n",
      "0.040000 0.857878 0.832938           0.024940\n",
      "0.050000 1.070759 1.039647           0.031112\n",
      "0.060000 1.282584 1.245338           0.037246\n",
      "0.070000 1.493142 1.449805           0.043337\n",
      "0.080000 1.702227 1.652849           0.049378\n",
      "0.090000 1.909632 1.854268           0.055364\n",
      "0.100000 2.115153 2.053863           0.061289\n",
      "0.110000 2.318586 2.251438           0.067148\n",
      "0.120000 2.519731 2.446798           0.072933\n",
      "0.130000 2.718389 2.639748           0.078641\n",
      "0.140000 2.914365 2.830100           0.084265\n",
      "0.150000 3.107464 3.017665           0.089800\n",
      "0.160000 3.297497 3.202257           0.095240\n",
      "0.170000 3.484276 3.383695           0.100580\n",
      "0.180000 3.667616 3.561800           0.105816\n",
      "0.190000 3.847336 3.736394           0.110942\n",
      "0.200000 4.023260 3.907307           0.115953\n",
      "0.210000 4.195213 4.074369           0.120844\n",
      "0.220000 4.363026 4.237415           0.125611\n",
      "0.230000 4.526533 4.396284           0.130249\n",
      "0.240000 4.685573 4.550819           0.134754\n",
      "0.250000 4.839989 4.700868           0.139121\n",
      "0.260000 4.989629 4.846282           0.143347\n",
      "0.270000 5.134344 4.986918           0.147427\n",
      "0.280000 5.273993 5.122636           0.151357\n",
      "0.290000 5.408436 5.253303           0.155133\n",
      "0.300000 5.537542 5.378789           0.158753\n",
      "0.310000 5.661183 5.498971           0.162213\n",
      "0.320000 5.779238 5.613729           0.165508\n",
      "0.330000 5.891589 5.722951           0.168638\n",
      "0.340000 5.998125 5.826528           0.171597\n",
      "0.350000 6.098742 5.924358           0.174385\n",
      "0.360000 6.193341 6.016344           0.176997\n",
      "0.370000 6.281827 6.102395           0.179432\n",
      "0.380000 6.364114 6.182426           0.181688\n",
      "0.390000 6.440121 6.256358           0.183762\n",
      "0.400000 6.509771 6.324118           0.185653\n",
      "0.410000 6.572998 6.385639           0.187359\n",
      "0.420000 6.629737 6.440859           0.188878\n",
      "0.430000 6.679934 6.489725           0.190210\n",
      "0.440000 6.723539 6.532187           0.191352\n",
      "0.450000 6.760508 6.568204           0.192304\n",
      "0.460000 6.790805 6.597740           0.193066\n",
      "0.470000 6.814401 6.620765           0.193636\n",
      "0.480000 6.831272 6.637257           0.194015\n",
      "0.490000 6.841401 6.647199           0.194202\n",
      "0.500000 6.844779 6.650581           0.194197\n",
      "0.510000 6.841401 6.647400           0.194001\n",
      "0.520000 6.831272 6.637659           0.193613\n",
      "0.530000 6.814401 6.621366           0.193035\n",
      "0.540000 6.790805 6.598539           0.192267\n",
      "0.550000 6.760508 6.569198           0.191310\n",
      "0.560000 6.723539 6.533374           0.190165\n",
      "0.570000 6.679934 6.491101           0.188833\n",
      "0.580000 6.629737 6.442420           0.187317\n",
      "0.590000 6.572998 6.387380           0.185618\n",
      "0.600000 6.509771 6.326035           0.183736\n",
      "0.610000 6.440121 6.258445           0.181676\n",
      "0.620000 6.364114 6.184676           0.179438\n",
      "0.630000 6.281827 6.104801           0.177026\n",
      "0.640000 6.193341 6.018900           0.174441\n",
      "0.650000 6.098742 5.927055           0.171687\n",
      "0.660000 5.998125 5.829359           0.168766\n",
      "0.670000 5.891589 5.725907           0.165682\n",
      "0.680000 5.779238 5.616800           0.162437\n",
      "0.690000 5.661183 5.502148           0.159036\n",
      "0.700000 5.537542 5.382061           0.155481\n",
      "0.710000 5.408436 5.256660           0.151776\n",
      "0.720000 5.273993 5.126067           0.147925\n",
      "0.730000 5.134344 4.990412           0.143932\n",
      "0.740000 4.989629 4.849827           0.139802\n",
      "0.750000 4.839989 4.704452           0.135537\n",
      "0.760000 4.685573 4.554430           0.131144\n",
      "0.770000 4.526533 4.399908           0.126625\n",
      "0.780000 4.363026 4.241040           0.121986\n",
      "0.790000 4.195213 4.077981           0.117232\n",
      "0.800000 4.023260 3.910893           0.112367\n",
      "0.810000 3.847336 3.739940           0.107396\n",
      "0.820000 3.667616 3.565291           0.102324\n",
      "0.830000 3.484276 3.387119           0.097157\n",
      "0.840000 3.297497 3.205598           0.091900\n",
      "0.850000 3.107464 3.020907           0.086557\n",
      "0.860000 2.914365 2.833230           0.081135\n",
      "0.870000 2.718389 2.642752           0.075638\n",
      "0.880000 2.519731 2.449659           0.070072\n",
      "0.890000 2.318586 2.254142           0.064444\n",
      "0.900000 2.115153 2.056395           0.058757\n",
      "0.910000 1.909632 1.856613           0.053019\n",
      "0.920000 1.702227 1.654992           0.047235\n",
      "0.930000 1.493142 1.451732           0.041411\n",
      "0.940000 1.282584 1.247032           0.035552\n",
      "0.950000 1.070759 1.041096           0.029664\n",
      "0.960000 0.857878 0.834125           0.023753\n",
      "0.970000 0.644151 0.626325           0.017826\n",
      "0.980000 0.429787 0.417900           0.011887\n",
      "0.990000 0.215000 0.209057           0.005943\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.89\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.221915 0.216152           0.005764\n",
      "0.020000 0.443611 0.432096           0.011515\n",
      "0.030000 0.664870 0.647621           0.017249\n",
      "0.040000 0.885472 0.862513           0.022959\n",
      "0.050000 1.105200 1.076560           0.028641\n",
      "0.060000 1.323838 1.289550           0.034288\n",
      "0.070000 1.541169 1.501274           0.039895\n",
      "0.080000 1.756979 1.711523           0.045456\n",
      "0.090000 1.971056 1.920089           0.050967\n",
      "0.100000 2.183187 2.126766           0.056421\n",
      "0.110000 2.393163 2.331349           0.061814\n",
      "0.120000 2.600778 2.533638           0.067140\n",
      "0.130000 2.805826 2.733432           0.072394\n",
      "0.140000 3.008106 2.930534           0.077572\n",
      "0.150000 3.207416 3.124750           0.082667\n",
      "0.160000 3.403561 3.315887           0.087675\n",
      "0.170000 3.596348 3.503757           0.092591\n",
      "0.180000 3.785585 3.688174           0.097411\n",
      "0.190000 3.971086 3.868957           0.102129\n",
      "0.200000 4.152668 4.045926           0.106742\n",
      "0.210000 4.330152 4.218907           0.111245\n",
      "0.220000 4.503363 4.387730           0.115633\n",
      "0.230000 4.672129 4.552227           0.119903\n",
      "0.240000 4.836285 4.712235           0.124050\n",
      "0.250000 4.995668 4.867598           0.128070\n",
      "0.260000 5.150120 5.018161           0.131960\n",
      "0.270000 5.299491 5.163775           0.135715\n",
      "0.280000 5.443631 5.304298           0.139333\n",
      "0.290000 5.582399 5.439589           0.142809\n",
      "0.300000 5.715657 5.569516           0.146142\n",
      "0.310000 5.843276 5.693949           0.149326\n",
      "0.320000 5.965127 5.812767           0.152360\n",
      "0.330000 6.081092 5.925851           0.155241\n",
      "0.340000 6.191055 6.033090           0.157965\n",
      "0.350000 6.294909 6.134378           0.160531\n",
      "0.360000 6.392550 6.229614           0.162936\n",
      "0.370000 6.483882 6.318705           0.165177\n",
      "0.380000 6.568816 6.401562           0.167254\n",
      "0.390000 6.647267 6.478104           0.169163\n",
      "0.400000 6.719158 6.548255           0.170904\n",
      "0.410000 6.784418 6.611945           0.172474\n",
      "0.420000 6.842983 6.669111           0.173872\n",
      "0.430000 6.894795 6.719697           0.175098\n",
      "0.440000 6.939802 6.763653           0.176149\n",
      "0.450000 6.977960 6.800935           0.177026\n",
      "0.460000 7.009232 6.831505           0.177727\n",
      "0.470000 7.033587 6.855335           0.178252\n",
      "0.480000 7.051000 6.872400           0.178600\n",
      "0.490000 7.061455 6.882683           0.178772\n",
      "0.500000 7.064941 6.886174           0.178768\n",
      "0.510000 7.061455 6.882868           0.178587\n",
      "0.520000 7.051000 6.872770           0.178230\n",
      "0.530000 7.033587 6.855889           0.177697\n",
      "0.540000 7.009232 6.832242           0.176990\n",
      "0.550000 6.977960 6.801851           0.176109\n",
      "0.560000 6.939802 6.764747           0.175055\n",
      "0.570000 6.894795 6.720965           0.173829\n",
      "0.580000 6.842983 6.670550           0.172433\n",
      "0.590000 6.784418 6.613550           0.170869\n",
      "0.600000 6.719158 6.550021           0.169137\n",
      "0.610000 6.647267 6.480027           0.167240\n",
      "0.620000 6.568816 6.403636           0.165180\n",
      "0.630000 6.483882 6.320923           0.162959\n",
      "0.640000 6.392550 6.231970           0.160580\n",
      "0.650000 6.294909 6.136864           0.158044\n",
      "0.660000 6.191055 6.035699           0.155356\n",
      "0.670000 6.081092 5.928575           0.152516\n",
      "0.680000 5.965127 5.815598           0.149529\n",
      "0.690000 5.843276 5.696878           0.146398\n",
      "0.700000 5.715657 5.572532           0.143125\n",
      "0.710000 5.582399 5.442684           0.139715\n",
      "0.720000 5.443631 5.307461           0.136170\n",
      "0.730000 5.299491 5.166996           0.132494\n",
      "0.740000 5.150120 5.021429           0.128692\n",
      "0.750000 4.995668 4.870902           0.124766\n",
      "0.760000 4.836285 4.715563           0.120722\n",
      "0.770000 4.672129 4.555567           0.116562\n",
      "0.780000 4.503363 4.391071           0.112292\n",
      "0.790000 4.330152 4.222237           0.107915\n",
      "0.800000 4.152668 4.049231           0.103437\n",
      "0.810000 3.971086 3.872225           0.098861\n",
      "0.820000 3.785585 3.691392           0.094192\n",
      "0.830000 3.596348 3.506912           0.089436\n",
      "0.840000 3.403561 3.318965           0.084596\n",
      "0.850000 3.207416 3.127738           0.079678\n",
      "0.860000 3.008106 2.933419           0.074686\n",
      "0.870000 2.805826 2.736200           0.069626\n",
      "0.880000 2.600778 2.536275           0.064503\n",
      "0.890000 2.393163 2.333842           0.059322\n",
      "0.900000 2.183187 2.129099           0.054088\n",
      "0.910000 1.971056 1.922250           0.048805\n",
      "0.920000 1.756979 1.713498           0.043481\n",
      "0.930000 1.541169 1.503050           0.038119\n",
      "0.940000 1.323838 1.291112           0.032726\n",
      "0.950000 1.105200 1.077894           0.027306\n",
      "0.960000 0.885472 0.863607           0.021865\n",
      "0.970000 0.664870 0.648461           0.016409\n",
      "0.980000 0.443611 0.432669           0.010942\n",
      "0.990000 0.221915 0.216444           0.005471\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.9\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.229050 0.223790           0.005260\n",
      "0.020000 0.457873 0.447365           0.010508\n",
      "0.030000 0.686245 0.670504           0.015741\n",
      "0.040000 0.913940 0.892988           0.020952\n",
      "0.050000 1.140732 1.114595           0.026137\n",
      "0.060000 1.366399 1.335109           0.031290\n",
      "0.070000 1.590717 1.554310           0.036407\n",
      "0.080000 1.813466 1.771984           0.041482\n",
      "0.090000 2.034425 1.987914           0.046511\n",
      "0.100000 2.253376 2.201887           0.051489\n",
      "0.110000 2.470103 2.413693           0.056410\n",
      "0.120000 2.684393 2.623122           0.061270\n",
      "0.130000 2.896033 2.829968           0.066065\n",
      "0.140000 3.104815 3.034026           0.070790\n",
      "0.150000 3.310534 3.235095           0.075439\n",
      "0.160000 3.512985 3.432976           0.080009\n",
      "0.170000 3.711969 3.627473           0.084496\n",
      "0.180000 3.907290 3.818396           0.088894\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.190000 4.098755 4.005555           0.093200\n",
      "0.200000 4.286175 4.188766           0.097410\n",
      "0.210000 4.469366 4.367847           0.101519\n",
      "0.220000 4.648145 4.542622           0.105523\n",
      "0.230000 4.822337 4.712918           0.109419\n",
      "0.240000 4.991770 4.878567           0.113204\n",
      "0.250000 5.156277 5.039405           0.116872\n",
      "0.260000 5.315695 5.195274           0.120422\n",
      "0.270000 5.469868 5.346019           0.123849\n",
      "0.280000 5.618642 5.491492           0.127150\n",
      "0.290000 5.761871 5.631548           0.130323\n",
      "0.300000 5.899414 5.766051           0.133364\n",
      "0.310000 6.031135 5.894866           0.136270\n",
      "0.320000 6.156904 6.017866           0.139038\n",
      "0.330000 6.276597 6.134931           0.141667\n",
      "0.340000 6.390096 6.245943           0.144153\n",
      "0.350000 6.497288 6.350794           0.146494\n",
      "0.360000 6.598069 6.449380           0.148689\n",
      "0.370000 6.692338 6.541603           0.150734\n",
      "0.380000 6.780002 6.627373           0.152629\n",
      "0.390000 6.860975 6.706604           0.154371\n",
      "0.400000 6.935177 6.779218           0.155959\n",
      "0.410000 7.002536 6.845143           0.157392\n",
      "0.420000 7.062983 6.904315           0.158668\n",
      "0.430000 7.116460 6.956674           0.159786\n",
      "0.440000 7.162914 7.002169           0.160746\n",
      "0.450000 7.202300 7.040754           0.161546\n",
      "0.460000 7.234577 7.072392           0.162185\n",
      "0.470000 7.259715 7.097050           0.162664\n",
      "0.480000 7.277688 7.114706           0.162982\n",
      "0.490000 7.288479 7.125340           0.163139\n",
      "0.500000 7.292077 7.128942           0.163135\n",
      "0.510000 7.288479 7.125509           0.162970\n",
      "0.520000 7.277688 7.115044           0.162644\n",
      "0.530000 7.259715 7.097557           0.162158\n",
      "0.540000 7.234577 7.073065           0.161512\n",
      "0.550000 7.202300 7.041591           0.160708\n",
      "0.560000 7.162914 7.003168           0.159746\n",
      "0.570000 7.116460 6.957833           0.158628\n",
      "0.580000 7.062983 6.905629           0.157354\n",
      "0.590000 7.002536 6.846610           0.155926\n",
      "0.600000 6.935177 6.780832           0.154345\n",
      "0.610000 6.860975 6.708361           0.152614\n",
      "0.620000 6.780002 6.629267           0.150734\n",
      "0.630000 6.692338 6.543630           0.148708\n",
      "0.640000 6.598069 6.451532           0.146536\n",
      "0.650000 6.497288 6.353066           0.144223\n",
      "0.660000 6.390096 6.248327           0.141769\n",
      "0.670000 6.276597 6.137420           0.139178\n",
      "0.680000 6.156904 6.020452           0.136452\n",
      "0.690000 6.031135 5.897541           0.133594\n",
      "0.700000 5.899414 5.768806           0.130608\n",
      "0.710000 5.761871 5.634376           0.127496\n",
      "0.720000 5.618642 5.494381           0.124261\n",
      "0.730000 5.469868 5.348961           0.120906\n",
      "0.740000 5.315695 5.198259           0.117436\n",
      "0.750000 5.156277 5.042423           0.113854\n",
      "0.760000 4.991770 4.881607           0.110163\n",
      "0.770000 4.822337 4.715970           0.106367\n",
      "0.780000 4.648145 4.545674           0.102471\n",
      "0.790000 4.469366 4.370889           0.098477\n",
      "0.800000 4.286175 4.191786           0.094390\n",
      "0.810000 4.098755 4.008541           0.090214\n",
      "0.820000 3.907290 3.821336           0.085954\n",
      "0.830000 3.711969 3.630356           0.081613\n",
      "0.840000 3.512985 3.435788           0.077197\n",
      "0.850000 3.310534 3.237825           0.072709\n",
      "0.860000 3.104815 3.036662           0.068154\n",
      "0.870000 2.896033 2.832497           0.063536\n",
      "0.880000 2.684393 2.625531           0.058861\n",
      "0.890000 2.470103 2.415970           0.054133\n",
      "0.900000 2.253376 2.204019           0.049357\n",
      "0.910000 2.034425 1.989888           0.044536\n",
      "0.920000 1.813466 1.773788           0.039678\n",
      "0.930000 1.590717 1.555932           0.034785\n",
      "0.940000 1.366399 1.336536           0.029863\n",
      "0.950000 1.140732 1.115815           0.024918\n",
      "0.960000 0.913940 0.893987           0.019953\n",
      "0.970000 0.686245 0.671272           0.014973\n",
      "0.980000 0.457873 0.447888           0.009985\n",
      "0.990000 0.229050 0.224057           0.004992\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.91\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.236410 0.231660           0.004750\n",
      "0.020000 0.472587 0.463097           0.009490\n",
      "0.030000 0.708298 0.694083           0.014215\n",
      "0.040000 0.943309 0.924388           0.018921\n",
      "0.050000 1.177390 1.153787           0.023603\n",
      "0.060000 1.410309 1.382052           0.028257\n",
      "0.070000 1.641836 1.608958           0.032878\n",
      "0.080000 1.871742 1.834281           0.037461\n",
      "0.090000 2.099802 2.057799           0.042003\n",
      "0.100000 2.325789 2.279291           0.046498\n",
      "0.110000 2.549481 2.498539           0.050942\n",
      "0.120000 2.770657 2.715325           0.055331\n",
      "0.130000 2.989098 2.929437           0.059661\n",
      "0.140000 3.204590 3.140662           0.063928\n",
      "0.150000 3.416919 3.348793           0.068126\n",
      "0.160000 3.625876 3.553622           0.072254\n",
      "0.170000 3.831255 3.754950           0.076305\n",
      "0.180000 4.032853 3.952576           0.080277\n",
      "0.190000 4.230470 4.146305           0.084165\n",
      "0.200000 4.423913 4.335946           0.087967\n",
      "0.210000 4.612990 4.521313           0.091677\n",
      "0.220000 4.797515 4.702221           0.095294\n",
      "0.230000 4.977305 4.878492           0.098812\n",
      "0.240000 5.152183 5.049953           0.102230\n",
      "0.250000 5.321976 5.216434           0.105542\n",
      "0.260000 5.486517 5.377769           0.108748\n",
      "0.270000 5.645644 5.533801           0.111843\n",
      "0.280000 5.799199 5.684375           0.114824\n",
      "0.290000 5.947031 5.829342           0.117689\n",
      "0.300000 6.088994 5.968560           0.120435\n",
      "0.310000 6.224948 6.101889           0.123059\n",
      "0.320000 6.354759 6.229200           0.125559\n",
      "0.330000 6.478298 6.350365           0.127933\n",
      "0.340000 6.595444 6.465266           0.130178\n",
      "0.350000 6.706081 6.573789           0.132292\n",
      "0.360000 6.810100 6.675826           0.134274\n",
      "0.370000 6.907398 6.771277           0.136121\n",
      "0.380000 6.997880 6.860048           0.137832\n",
      "0.390000 7.081455 6.942050           0.139405\n",
      "0.400000 7.158042 7.017203           0.140839\n",
      "0.410000 7.227565 7.085432           0.142133\n",
      "0.420000 7.289955 7.146669           0.143285\n",
      "0.430000 7.345150 7.200855           0.144295\n",
      "0.440000 7.393097 7.247936           0.145161\n",
      "0.450000 7.433748 7.287865           0.145883\n",
      "0.460000 7.467063 7.320602           0.146461\n",
      "0.470000 7.493008 7.346115           0.146893\n",
      "0.480000 7.511559 7.364379           0.147180\n",
      "0.490000 7.522697 7.375375           0.147322\n",
      "0.500000 7.526411 7.379093           0.147318\n",
      "0.510000 7.522697 7.375528           0.147169\n",
      "0.520000 7.511559 7.364684           0.146875\n",
      "0.530000 7.493008 7.346573           0.146436\n",
      "0.540000 7.467063 7.321210           0.145853\n",
      "0.550000 7.433748 7.288622           0.145126\n",
      "0.560000 7.393097 7.248840           0.144258\n",
      "0.570000 7.345150 7.201903           0.143247\n",
      "0.580000 7.289955 7.147858           0.142097\n",
      "0.590000 7.227565 7.086757           0.140807\n",
      "0.600000 7.158042 7.018662           0.139380\n",
      "0.610000 7.081455 6.943638           0.137817\n",
      "0.620000 6.997880 6.861761           0.136119\n",
      "0.630000 6.907398 6.773109           0.134289\n",
      "0.640000 6.810100 6.677772           0.132328\n",
      "0.650000 6.706081 6.575843           0.130238\n",
      "0.660000 6.595444 6.467421           0.128023\n",
      "0.670000 6.478298 6.352615           0.125683\n",
      "0.680000 6.354759 6.231538           0.123221\n",
      "0.690000 6.224948 6.104308           0.120641\n",
      "0.700000 6.088994 5.971051           0.117944\n",
      "0.710000 5.947031 5.831898           0.115133\n",
      "0.720000 5.799199 5.686987           0.112212\n",
      "0.730000 5.645644 5.536461           0.109183\n",
      "0.740000 5.486517 5.380468           0.106049\n",
      "0.750000 5.321976 5.219162           0.102814\n",
      "0.760000 5.152183 5.052702           0.099481\n",
      "0.770000 4.977305 4.881252           0.096053\n",
      "0.780000 4.797515 4.704981           0.092534\n",
      "0.790000 4.612990 4.524063           0.088928\n",
      "0.800000 4.423913 4.338676           0.085237\n",
      "0.810000 4.230470 4.149004           0.081466\n",
      "0.820000 4.032853 3.955234           0.077619\n",
      "0.830000 3.831255 3.757556           0.073699\n",
      "0.840000 3.625876 3.556165           0.069711\n",
      "0.850000 3.416919 3.351261           0.065658\n",
      "0.860000 3.204590 3.143045           0.061545\n",
      "0.870000 2.989098 2.931723           0.057375\n",
      "0.880000 2.770657 2.717503           0.053153\n",
      "0.890000 2.549481 2.500597           0.048884\n",
      "0.900000 2.325789 2.281219           0.044570\n",
      "0.910000 2.099802 2.059584           0.040218\n",
      "0.920000 1.871742 1.835912           0.035830\n",
      "0.930000 1.641836 1.610424           0.031412\n",
      "0.940000 1.410309 1.383341           0.026967\n",
      "0.950000 1.177390 1.154889           0.022501\n",
      "0.960000 0.943309 0.925292           0.018018\n",
      "0.970000 0.708298 0.694776           0.013521\n",
      "0.980000 0.472587 0.463571           0.009017\n",
      "0.990000 0.236410 0.231902           0.004508\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.92\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.244004 0.239769           0.004235\n",
      "0.020000 0.487768 0.479307           0.008461\n",
      "0.030000 0.731050 0.718376           0.012673\n",
      "0.040000 0.973610 0.956741           0.016869\n",
      "0.050000 1.215210 1.194167           0.021043\n",
      "0.060000 1.455610 1.430418           0.025192\n",
      "0.070000 1.694574 1.665262           0.029312\n",
      "0.080000 1.931866 1.898468           0.033398\n",
      "0.090000 2.167251 2.129804           0.037447\n",
      "0.100000 2.400498 2.359043           0.041454\n",
      "0.110000 2.631375 2.585958           0.045417\n",
      "0.120000 2.859655 2.810325           0.049330\n",
      "0.130000 3.085114 3.031923           0.053190\n",
      "0.140000 3.307527 3.250533           0.056994\n",
      "0.150000 3.526677 3.465940           0.060737\n",
      "0.160000 3.742346 3.677929           0.064417\n",
      "0.170000 3.954322 3.886293           0.068029\n",
      "0.180000 4.162395 4.090826           0.071570\n",
      "0.190000 4.366361 4.291325           0.075036\n",
      "0.200000 4.566018 4.487592           0.078425\n",
      "0.210000 4.761168 4.679435           0.081733\n",
      "0.220000 4.951620 4.866662           0.084957\n",
      "0.230000 5.137185 5.049091           0.088094\n",
      "0.240000 5.317680 5.226539           0.091141\n",
      "0.250000 5.492928 5.398833           0.094094\n",
      "0.260000 5.662754 5.565802           0.096952\n",
      "0.270000 5.826993 5.727281           0.099711\n",
      "0.280000 5.985480 5.883111           0.102369\n",
      "0.290000 6.138061 6.033138           0.104923\n",
      "0.300000 6.284584 6.177213           0.107371\n",
      "0.310000 6.424905 6.315195           0.109711\n",
      "0.320000 6.558885 6.446946           0.111939\n",
      "0.330000 6.686393 6.572338           0.114056\n",
      "0.340000 6.807302 6.691245           0.116057\n",
      "0.350000 6.921493 6.803551           0.117942\n",
      "0.360000 7.028853 6.909145           0.119709\n",
      "0.370000 7.129277 7.007921           0.121355\n",
      "0.380000 7.222665 7.099784           0.122881\n",
      "0.390000 7.308925 7.184641           0.124283\n",
      "0.400000 7.387972 7.262410           0.125562\n",
      "0.410000 7.459728 7.333013           0.126715\n",
      "0.420000 7.524122 7.396379           0.127742\n",
      "0.430000 7.581090 7.452448           0.128642\n",
      "0.440000 7.630577 7.501163           0.129415\n",
      "0.450000 7.672534 7.542476           0.130058\n",
      "0.460000 7.706919 7.576346           0.130573\n",
      "0.470000 7.733698 7.602739           0.130959\n",
      "0.480000 7.752844 7.621630           0.131215\n",
      "0.490000 7.764340 7.632999           0.131341\n",
      "0.500000 7.768173 7.636836           0.131337\n",
      "0.510000 7.764340 7.633136           0.131204\n",
      "0.520000 7.752844 7.621903           0.130942\n",
      "0.530000 7.733698 7.603147           0.130550\n",
      "0.540000 7.706919 7.576888           0.130030\n",
      "0.550000 7.672534 7.543151           0.129383\n",
      "0.560000 7.630577 7.501969           0.128608\n",
      "0.570000 7.581090 7.453383           0.127708\n",
      "0.580000 7.524122 7.397440           0.126682\n",
      "0.590000 7.459728 7.334196           0.125532\n",
      "0.600000 7.387972 7.263712           0.124260\n",
      "0.610000 7.308925 7.186059           0.122866\n",
      "0.620000 7.222665 7.101312           0.121352\n",
      "0.630000 7.129277 7.009556           0.119721\n",
      "0.640000 7.028853 6.910881           0.117972\n",
      "0.650000 6.921493 6.805384           0.116109\n",
      "0.660000 6.807302 6.693168           0.114134\n",
      "0.670000 6.686393 6.574345           0.112048\n",
      "0.680000 6.558885 6.449032           0.109853\n",
      "0.690000 6.424905 6.317353           0.107553\n",
      "0.700000 6.284584 6.179436           0.105148\n",
      "0.710000 6.138061 6.035419           0.102642\n",
      "0.720000 5.985480 5.885442           0.100038\n",
      "0.730000 5.826993 5.729655           0.097337\n",
      "0.740000 5.662754 5.568211           0.094544\n",
      "0.750000 5.492928 5.401268           0.091660\n",
      "0.760000 5.317680 5.228992           0.088688\n",
      "0.770000 5.137185 5.051553           0.085632\n",
      "0.780000 4.951620 4.869125           0.082495\n",
      "0.790000 4.761168 4.681889           0.079280\n",
      "0.800000 4.566018 4.490028           0.075989\n",
      "0.810000 4.366361 4.293733           0.072628\n",
      "0.820000 4.162395 4.093198           0.069198\n",
      "0.830000 3.954322 3.888619           0.065703\n",
      "0.840000 3.742346 3.680198           0.062148\n",
      "0.850000 3.526677 3.468142           0.058534\n",
      "0.860000 3.307527 3.252660           0.054867\n",
      "0.870000 3.085114 3.033963           0.051150\n",
      "0.880000 2.859655 2.812269           0.047386\n",
      "0.890000 2.631375 2.587795           0.043580\n",
      "0.900000 2.400498 2.360763           0.039734\n",
      "0.910000 2.167251 2.131397           0.035854\n",
      "0.920000 1.931866 1.899924           0.031942\n",
      "0.930000 1.694574 1.666571           0.028004\n",
      "0.940000 1.455610 1.431569           0.024041\n",
      "0.950000 1.215210 1.195150           0.020060\n",
      "0.960000 0.973610 0.957547           0.016063\n",
      "0.970000 0.731050 0.718995           0.012054\n",
      "0.980000 0.487768 0.479729           0.008038\n",
      "0.990000 0.244004 0.239985           0.004019\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.93\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.251839 0.248124           0.003715\n",
      "0.020000 0.503429 0.496008           0.007422\n",
      "0.030000 0.754523 0.743406           0.011118\n",
      "0.040000 1.004872 0.990074           0.014798\n",
      "0.050000 1.254229 1.235769           0.018460\n",
      "0.060000 1.502349 1.480249           0.022100\n",
      "0.070000 1.748986 1.723272           0.025714\n",
      "0.080000 1.993897 1.964599           0.029298\n",
      "0.090000 2.236840 2.203990           0.032850\n",
      "0.100000 2.477576 2.441210           0.036365\n",
      "0.110000 2.715866 2.676025           0.039841\n",
      "0.120000 2.951477 2.908203           0.043274\n",
      "0.130000 3.184174 3.137514           0.046660\n",
      "0.140000 3.413729 3.363732           0.049997\n",
      "0.150000 3.639916 3.586635           0.053281\n",
      "0.160000 3.862510 3.806001           0.056508\n",
      "0.170000 4.081292 4.021615           0.059677\n",
      "0.180000 4.296047 4.233263           0.062783\n",
      "0.190000 4.506561 4.440737           0.065824\n",
      "0.200000 4.712629 4.643832           0.068797\n",
      "0.210000 4.914045 4.842346           0.071699\n",
      "0.220000 5.110613 5.036085           0.074527\n",
      "0.230000 5.302136 5.224857           0.077279\n",
      "0.240000 5.488427 5.408475           0.079952\n",
      "0.250000 5.669301 5.586759           0.082543\n",
      "0.260000 5.844581 5.759532           0.085049\n",
      "0.270000 6.014093 5.926623           0.087470\n",
      "0.280000 6.177669 6.087868           0.089801\n",
      "0.290000 6.335149 6.243108           0.092042\n",
      "0.300000 6.486377 6.392188           0.094189\n",
      "0.310000 6.631204 6.534963           0.096241\n",
      "0.320000 6.769486 6.671290           0.098196\n",
      "0.330000 6.901088 6.801035           0.100053\n",
      "0.340000 7.025879 6.924071           0.101808\n",
      "0.350000 7.143737 7.040275           0.103462\n",
      "0.360000 7.254544 7.149533           0.105012\n",
      "0.370000 7.358192 7.251736           0.106456\n",
      "0.380000 7.454579 7.346785           0.107794\n",
      "0.390000 7.543609 7.434584           0.109024\n",
      "0.400000 7.625194 7.515048           0.110146\n",
      "0.410000 7.699254 7.588096           0.111158\n",
      "0.420000 7.765715 7.653657           0.112059\n",
      "0.430000 7.824513 7.711665           0.112848\n",
      "0.440000 7.875589 7.762064           0.113526\n",
      "0.450000 7.918893 7.804803           0.114090\n",
      "0.460000 7.954382 7.839840           0.114542\n",
      "0.470000 7.982021 7.867141           0.114880\n",
      "0.480000 8.001782 7.886678           0.115104\n",
      "0.490000 8.013647 7.898432           0.115215\n",
      "0.500000 8.017603 7.902391           0.115212\n",
      "0.510000 8.013647 7.898552           0.115095\n",
      "0.520000 8.001782 7.886917           0.114865\n",
      "0.530000 7.982021 7.867499           0.114521\n",
      "0.540000 7.954382 7.840317           0.114065\n",
      "0.550000 7.918893 7.805396           0.113497\n",
      "0.560000 7.875589 7.762772           0.112818\n",
      "0.570000 7.824513 7.712486           0.112027\n",
      "0.580000 7.765715 7.654588           0.111128\n",
      "0.590000 7.699254 7.589135           0.110119\n",
      "0.600000 7.625194 7.516191           0.109003\n",
      "0.610000 7.543609 7.435828           0.107780\n",
      "0.620000 7.454579 7.348127           0.106452\n",
      "0.630000 7.358192 7.253171           0.105021\n",
      "0.640000 7.254544 7.151057           0.103487\n",
      "0.650000 7.143737 7.041884           0.101853\n",
      "0.660000 7.025879 6.925759           0.100120\n",
      "0.670000 6.901088 6.802798           0.098290\n",
      "0.680000 6.769486 6.673121           0.096365\n",
      "0.690000 6.631204 6.536857           0.094347\n",
      "0.700000 6.486377 6.394140           0.092237\n",
      "0.710000 6.335149 6.245110           0.090039\n",
      "0.720000 6.177669 6.089915           0.087755\n",
      "0.730000 6.014093 5.928707           0.085386\n",
      "0.740000 5.844581 5.761646           0.082935\n",
      "0.750000 5.669301 5.588897           0.080405\n",
      "0.760000 5.488427 5.410629           0.077798\n",
      "0.770000 5.302136 5.227019           0.075118\n",
      "0.780000 5.110613 5.038247           0.072365\n",
      "0.790000 4.914045 4.844501           0.069545\n",
      "0.800000 4.712629 4.645970           0.066659\n",
      "0.810000 4.506561 4.442852           0.063710\n",
      "0.820000 4.296047 4.235346           0.060701\n",
      "0.830000 4.081292 4.023657           0.057636\n",
      "0.840000 3.862510 3.807993           0.054516\n",
      "0.850000 3.639916 3.588569           0.051347\n",
      "0.860000 3.413729 3.365599           0.048130\n",
      "0.870000 3.184174 3.139305           0.044869\n",
      "0.880000 2.951477 2.909909           0.041568\n",
      "0.890000 2.715866 2.677638           0.038229\n",
      "0.900000 2.477576 2.442720           0.034855\n",
      "0.910000 2.236840 2.205389           0.031451\n",
      "0.920000 1.993897 1.965877           0.028020\n",
      "0.930000 1.748986 1.724421           0.024565\n",
      "0.940000 1.502349 1.481260           0.021089\n",
      "0.950000 1.254229 1.236633           0.017597\n",
      "0.960000 1.004872 0.990782           0.014090\n",
      "0.970000 0.754523 0.743949           0.010574\n",
      "0.980000 0.503429 0.496378           0.007051\n",
      "0.990000 0.251839 0.248314           0.003525\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.9400000000000001\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.259922 0.256731           0.003191\n",
      "0.020000 0.519588 0.513213           0.006375\n",
      "0.030000 0.778741 0.769192           0.009550\n",
      "0.040000 1.037126 1.024415           0.012711\n",
      "0.050000 1.294487 1.278630           0.015857\n",
      "0.060000 1.550570 1.531587           0.018983\n",
      "0.070000 1.805124 1.783036           0.022087\n",
      "0.080000 2.057896 2.032729           0.025166\n",
      "0.090000 2.308637 2.280419           0.028217\n",
      "0.100000 2.557099 2.525862           0.031237\n",
      "0.110000 2.803038 2.768816           0.034222\n",
      "0.120000 3.046211 3.009040           0.037171\n",
      "0.130000 3.286378 3.246298           0.040080\n",
      "0.140000 3.523301 3.480355           0.042946\n",
      "0.150000 3.756747 3.710981           0.045766\n",
      "0.160000 3.986486 3.937947           0.048539\n",
      "0.170000 4.212291 4.161030           0.051261\n",
      "0.180000 4.433938 4.380009           0.053929\n",
      "0.190000 4.651210 4.594669           0.056541\n",
      "0.200000 4.863892 4.804797           0.059095\n",
      "0.210000 5.071773 5.010186           0.061587\n",
      "0.220000 5.274650 5.210633           0.064017\n",
      "0.230000 5.472320 5.405940           0.066380\n",
      "0.240000 5.664591 5.595915           0.068676\n",
      "0.250000 5.851271 5.780370           0.070901\n",
      "0.260000 6.032177 5.959122           0.073054\n",
      "0.270000 6.207129 6.131996           0.075133\n",
      "0.280000 6.375956 6.298820           0.077136\n",
      "0.290000 6.538491 6.459430           0.079060\n",
      "0.300000 6.694573 6.613668           0.080905\n",
      "0.310000 6.844048 6.761380           0.082668\n",
      "0.320000 6.986769 6.902421           0.084347\n",
      "0.330000 7.122594 7.036653           0.085942\n",
      "0.340000 7.251391 7.163941           0.087450\n",
      "0.350000 7.373032 7.284162           0.088870\n",
      "0.360000 7.487396 7.397195           0.090201\n",
      "0.370000 7.594371 7.502929           0.091442\n",
      "0.380000 7.693851 7.601260           0.092591\n",
      "0.390000 7.785738 7.692090           0.093648\n",
      "0.400000 7.869942 7.775331           0.094611\n",
      "0.410000 7.946379 7.850899           0.095480\n",
      "0.420000 8.014974 7.918720           0.096254\n",
      "0.430000 8.075659 7.978727           0.096932\n",
      "0.440000 8.128375 8.030861           0.097514\n",
      "0.450000 8.173068 8.075070           0.097999\n",
      "0.460000 8.209696 8.111310           0.098387\n",
      "0.470000 8.238222 8.139545           0.098677\n",
      "0.480000 8.258618 8.159748           0.098870\n",
      "0.490000 8.270864 8.171899           0.098965\n",
      "0.500000 8.274947 8.175985           0.098962\n",
      "0.510000 8.270864 8.172002           0.098862\n",
      "0.520000 8.258618 8.159954           0.098664\n",
      "0.530000 8.238222 8.139853           0.098369\n",
      "0.540000 8.209696 8.111719           0.097977\n",
      "0.550000 8.173068 8.075579           0.097489\n",
      "0.560000 8.128375 8.031469           0.096905\n",
      "0.570000 8.075659 7.979433           0.096227\n",
      "0.580000 8.014974 7.919520           0.095454\n",
      "0.590000 7.946379 7.851792           0.094587\n",
      "0.600000 7.869942 7.776314           0.093628\n",
      "0.610000 7.785738 7.693160           0.092578\n",
      "0.620000 7.693851 7.602413           0.091438\n",
      "0.630000 7.594371 7.504163           0.090208\n",
      "0.640000 7.487396 7.398505           0.088891\n",
      "0.650000 7.373032 7.285545           0.087487\n",
      "0.660000 7.251391 7.165393           0.085998\n",
      "0.670000 7.122594 7.038168           0.084426\n",
      "0.680000 6.986769 6.903996           0.082773\n",
      "0.690000 6.844048 6.763009           0.081039\n",
      "0.700000 6.694573 6.615345           0.079227\n",
      "0.710000 6.538491 6.461151           0.077339\n",
      "0.720000 6.375956 6.300579           0.075377\n",
      "0.730000 6.207129 6.133787           0.073342\n",
      "0.740000 6.032177 5.960940           0.071237\n",
      "0.750000 5.851271 5.782207           0.069064\n",
      "0.760000 5.664591 5.597766           0.066825\n",
      "0.770000 5.472320 5.407798           0.064522\n",
      "0.780000 5.274650 5.212491           0.062158\n",
      "0.790000 5.071773 5.012038           0.059735\n",
      "0.800000 4.863892 4.806635           0.057256\n",
      "0.810000 4.651210 4.596487           0.054723\n",
      "0.820000 4.433938 4.381799           0.052139\n",
      "0.830000 4.212291 4.162785           0.049506\n",
      "0.840000 3.986486 3.939659           0.046827\n",
      "0.850000 3.756747 3.712643           0.044104\n",
      "0.860000 3.523301 3.481960           0.041341\n",
      "0.870000 3.286378 3.247837           0.038540\n",
      "0.880000 3.046211 3.010507           0.035704\n",
      "0.890000 2.803038 2.770202           0.032836\n",
      "0.900000 2.557099 2.527160           0.029939\n",
      "0.910000 2.308637 2.281622           0.027015\n",
      "0.920000 2.057896 2.033828           0.024068\n",
      "0.930000 1.805124 1.784024           0.021100\n",
      "0.940000 1.550570 1.532456           0.018114\n",
      "0.950000 1.294487 1.279372           0.015114\n",
      "0.960000 1.037126 1.025023           0.012103\n",
      "0.970000 0.778741 0.769659           0.009083\n",
      "0.980000 0.519588 0.513532           0.006057\n",
      "0.990000 0.259922 0.256894           0.003028\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.9500000000000001\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.268262 0.265599           0.002664\n",
      "0.020000 0.536260 0.530938           0.005322\n",
      "0.030000 0.803728 0.795756           0.007972\n",
      "0.040000 1.070403 1.059792           0.010611\n",
      "0.050000 1.336022 1.322785           0.013237\n",
      "0.060000 1.600322 1.584476           0.015846\n",
      "0.070000 1.863043 1.844606           0.018438\n",
      "0.080000 2.123926 2.102918           0.021008\n",
      "0.090000 2.382712 2.359157           0.023554\n",
      "0.100000 2.639147 2.613072           0.026075\n",
      "0.110000 2.892977 2.864410           0.028567\n",
      "0.120000 3.143952 3.112924           0.031029\n",
      "0.130000 3.391825 3.358368           0.033457\n",
      "0.140000 3.636350 3.600501           0.035849\n",
      "0.150000 3.877287 3.839083           0.038204\n",
      "0.160000 4.114397 4.073879           0.040518\n",
      "0.170000 4.347447 4.304657           0.042790\n",
      "0.180000 4.576206 4.531189           0.045017\n",
      "0.190000 4.800450 4.753252           0.047198\n",
      "0.200000 5.019955 4.970626           0.049330\n",
      "0.210000 5.234507 5.183097           0.051410\n",
      "0.220000 5.443893 5.390455           0.053438\n",
      "0.230000 5.647906 5.592495           0.055411\n",
      "0.240000 5.846346 5.789018           0.057327\n",
      "0.250000 6.039016 5.979831           0.059185\n",
      "0.260000 6.225726 6.164744           0.060982\n",
      "0.270000 6.406292 6.343574           0.062718\n",
      "0.280000 6.580536 6.516147           0.064390\n",
      "0.290000 6.748286 6.682290           0.065996\n",
      "0.300000 6.909376 6.841840           0.067536\n",
      "0.310000 7.063647 6.994640           0.069007\n",
      "0.320000 7.210947 7.140538           0.070409\n",
      "0.330000 7.351131 7.279391           0.071740\n",
      "0.340000 7.484060 7.411062           0.072999\n",
      "0.350000 7.609604 7.535420           0.074184\n",
      "0.360000 7.727638 7.652342           0.075295\n",
      "0.370000 7.838045 7.761714           0.076331\n",
      "0.380000 7.940717 7.863427           0.077290\n",
      "0.390000 8.035553 7.957380           0.078172\n",
      "0.400000 8.122458 8.043482           0.078977\n",
      "0.410000 8.201348 8.121646           0.079702\n",
      "0.420000 8.272144 8.191796           0.080348\n",
      "0.430000 8.334776 8.253862           0.080914\n",
      "0.440000 8.389183 8.307784           0.081400\n",
      "0.450000 8.435311 8.353506           0.081804\n",
      "0.460000 8.473114 8.390986           0.082128\n",
      "0.470000 8.502555 8.420185           0.082370\n",
      "0.480000 8.523605 8.441074           0.082531\n",
      "0.490000 8.536244 8.453633           0.082611\n",
      "0.500000 8.540458 8.457850           0.082608\n",
      "0.510000 8.536244 8.453719           0.082524\n",
      "0.520000 8.523605 8.441246           0.082359\n",
      "0.530000 8.502555 8.420442           0.082113\n",
      "0.540000 8.473114 8.391328           0.081786\n",
      "0.550000 8.435311 8.353932           0.081379\n",
      "0.560000 8.389183 8.308292           0.080891\n",
      "0.570000 8.334776 8.254452           0.080325\n",
      "0.580000 8.272144 8.192464           0.079679\n",
      "0.590000 8.201348 8.122392           0.078956\n",
      "0.600000 8.122458 8.044303           0.078156\n",
      "0.610000 8.035553 7.958274           0.077279\n",
      "0.620000 7.940717 7.864390           0.076327\n",
      "0.630000 7.838045 7.762744           0.075301\n",
      "0.640000 7.727638 7.653437           0.074201\n",
      "0.650000 7.609604 7.536575           0.073029\n",
      "0.660000 7.484060 7.412274           0.071786\n",
      "0.670000 7.351131 7.280657           0.070474\n",
      "0.680000 7.210947 7.141853           0.069094\n",
      "0.690000 7.063647 6.996000           0.067647\n",
      "0.700000 6.909376 6.843241           0.066134\n",
      "0.710000 6.748286 6.683727           0.064558\n",
      "0.720000 6.580536 6.517616           0.062920\n",
      "0.730000 6.406292 6.345071           0.061222\n",
      "0.740000 6.225726 6.166262           0.059464\n",
      "0.750000 6.039016 5.981365           0.057650\n",
      "0.760000 5.846346 5.790565           0.055781\n",
      "0.770000 5.647906 5.594047           0.053859\n",
      "0.780000 5.443893 5.392007           0.051886\n",
      "0.790000 5.234507 5.184643           0.049864\n",
      "0.800000 5.019955 4.972161           0.047794\n",
      "0.810000 4.800450 4.754770           0.045680\n",
      "0.820000 4.576206 4.532684           0.043522\n",
      "0.830000 4.347447 4.306122           0.041324\n",
      "0.840000 4.114397 4.075309           0.039088\n",
      "0.850000 3.877287 3.840471           0.036815\n",
      "0.860000 3.636350 3.601841           0.034509\n",
      "0.870000 3.391825 3.359654           0.032171\n",
      "0.880000 3.143952 3.114149           0.029804\n",
      "0.890000 2.892977 2.865567           0.027410\n",
      "0.900000 2.639147 2.614156           0.024991\n",
      "0.910000 2.382712 2.360161           0.022550\n",
      "0.920000 2.123926 2.103835           0.020090\n",
      "0.930000 1.863043 1.845430           0.017613\n",
      "0.940000 1.600322 1.585202           0.015121\n",
      "0.950000 1.336022 1.323405           0.012617\n",
      "0.960000 1.070403 1.060301           0.010103\n",
      "0.970000 0.803728 0.796147           0.007581\n",
      "0.980000 0.536260 0.531204           0.005056\n",
      "0.990000 0.268262 0.265735           0.002528\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.96\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.276867 0.274733           0.002134\n",
      "0.020000 0.553461 0.549198           0.004263\n",
      "0.030000 0.829508 0.823123           0.006386\n",
      "0.040000 1.104737 1.096238           0.008500\n",
      "0.050000 1.378876 1.368273           0.010603\n",
      "0.060000 1.651654 1.638960           0.012693\n",
      "0.070000 1.922802 1.908033           0.014769\n",
      "0.080000 2.192052 2.175224           0.016828\n",
      "0.090000 2.459139 2.440271           0.018868\n",
      "0.100000 2.723799 2.702912           0.020887\n",
      "0.110000 2.985771 2.962888           0.022883\n",
      "0.120000 3.244797 3.219942           0.024855\n",
      "0.130000 3.500620 3.473820           0.026800\n",
      "0.140000 3.752989 3.724272           0.028716\n",
      "0.150000 4.001654 3.971051           0.030602\n",
      "0.160000 4.246369 4.213913           0.032456\n",
      "0.170000 4.486894 4.452618           0.034276\n",
      "0.180000 4.722991 4.686931           0.036060\n",
      "0.190000 4.954427 4.916620           0.037807\n",
      "0.200000 5.180974 5.141460           0.039514\n",
      "0.210000 5.402407 5.361226           0.041181\n",
      "0.220000 5.618510 5.575704           0.042805\n",
      "0.230000 5.829067 5.784681           0.044386\n",
      "0.240000 6.033871 5.987951           0.045921\n",
      "0.250000 6.232721 6.185313           0.047409\n",
      "0.260000 6.425421 6.376572           0.048849\n",
      "0.270000 6.611778 6.561540           0.050239\n",
      "0.280000 6.791611 6.740034           0.051578\n",
      "0.290000 6.964742 6.911877           0.052864\n",
      "0.300000 7.130999 7.076901           0.054098\n",
      "0.310000 7.290218 7.234942           0.055276\n",
      "0.320000 7.442243 7.385844           0.056399\n",
      "0.330000 7.586924 7.529458           0.057465\n",
      "0.340000 7.724117 7.665643           0.058474\n",
      "0.350000 7.853687 7.794264           0.059423\n",
      "0.360000 7.975507 7.915194           0.060313\n",
      "0.370000 8.089456 8.028313           0.061143\n",
      "0.380000 8.195421 8.133510           0.061911\n",
      "0.390000 8.293299 8.230681           0.062618\n",
      "0.400000 8.382992 8.319730           0.063262\n",
      "0.410000 8.464412 8.400569           0.063843\n",
      "0.420000 8.537479 8.473118           0.064360\n",
      "0.430000 8.602120 8.537306           0.064814\n",
      "0.440000 8.658272 8.593069           0.065203\n",
      "0.450000 8.705879 8.640352           0.065527\n",
      "0.460000 8.744895 8.679109           0.065786\n",
      "0.470000 8.775281 8.709300           0.065981\n",
      "0.480000 8.797006 8.730897           0.066109\n",
      "0.490000 8.810050 8.743877           0.066173\n",
      "0.500000 8.814399 8.748228           0.066171\n",
      "0.510000 8.810050 8.743946           0.066104\n",
      "0.520000 8.797006 8.731035           0.065971\n",
      "0.530000 8.775281 8.709506           0.065774\n",
      "0.540000 8.744895 8.679383           0.065512\n",
      "0.550000 8.705879 8.640694           0.065186\n",
      "0.560000 8.658272 8.593476           0.064796\n",
      "0.570000 8.602120 8.537778           0.064342\n",
      "0.580000 8.537479 8.473654           0.063825\n",
      "0.590000 8.464412 8.401167           0.063245\n",
      "0.600000 8.382992 8.320388           0.062604\n",
      "0.610000 8.293299 8.231397           0.061902\n",
      "0.620000 8.195421 8.134282           0.061139\n",
      "0.630000 8.089456 8.029139           0.060317\n",
      "0.640000 7.975507 7.916071           0.059436\n",
      "0.650000 7.853687 7.795190           0.058498\n",
      "0.660000 7.724117 7.666615           0.057502\n",
      "0.670000 7.586924 7.530473           0.056451\n",
      "0.680000 7.442243 7.386898           0.055345\n",
      "0.690000 7.290218 7.236032           0.054186\n",
      "0.700000 7.130999 7.078024           0.052975\n",
      "0.710000 6.964742 6.913029           0.051712\n",
      "0.720000 6.791611 6.741211           0.050400\n",
      "0.730000 6.611778 6.562739           0.049039\n",
      "0.740000 6.425421 6.377789           0.047632\n",
      "0.750000 6.232721 6.186543           0.046179\n",
      "0.760000 6.033871 5.989190           0.044682\n",
      "0.770000 5.829067 5.785925           0.043142\n",
      "0.780000 5.618510 5.576948           0.041561\n",
      "0.790000 5.402407 5.362466           0.039941\n",
      "0.800000 5.180974 5.142690           0.038284\n",
      "0.810000 4.954427 4.917837           0.036590\n",
      "0.820000 4.722991 4.688129           0.034862\n",
      "0.830000 4.486894 4.453793           0.033101\n",
      "0.840000 4.246369 4.215059           0.031310\n",
      "0.850000 4.001654 3.972164           0.029490\n",
      "0.860000 3.752989 3.725346           0.027642\n",
      "0.870000 3.500620 3.474851           0.025769\n",
      "0.880000 3.244797 3.220924           0.023873\n",
      "0.890000 2.985771 2.963816           0.021955\n",
      "0.900000 2.723799 2.703781           0.020018\n",
      "0.910000 2.459139 2.441076           0.018063\n",
      "0.920000 2.192052 2.175959           0.016092\n",
      "0.930000 1.922802 1.908694           0.014108\n",
      "0.940000 1.651654 1.639542           0.012112\n",
      "0.950000 1.378876 1.368770           0.010106\n",
      "0.960000 1.104737 1.096645           0.008092\n",
      "0.970000 0.829508 0.823435           0.006073\n",
      "0.980000 0.553461 0.549411           0.004050\n",
      "0.990000 0.276867 0.274842           0.002025\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.97\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.285745 0.284143           0.001602\n",
      "0.020000 0.571208 0.568008           0.003200\n",
      "0.030000 0.856107 0.851314           0.004793\n",
      "0.040000 1.140162 1.133781           0.006380\n",
      "0.050000 1.423091 1.415132           0.007959\n",
      "0.060000 1.704615 1.695087           0.009528\n",
      "0.070000 1.984458 1.973372           0.011086\n",
      "0.080000 2.262342 2.249710           0.012632\n",
      "0.090000 2.537993 2.523830           0.014163\n",
      "0.100000 2.811140 2.795461           0.015679\n",
      "0.110000 3.081513 3.064335           0.017177\n",
      "0.120000 3.348844 3.330187           0.018657\n",
      "0.130000 3.612870 3.592753           0.020117\n",
      "0.140000 3.873331 3.851776           0.021556\n",
      "0.150000 4.129970 4.106998           0.022972\n",
      "0.160000 4.382533 4.358170           0.024363\n",
      "0.170000 4.630770 4.605041           0.025729\n",
      "0.180000 4.874438 4.847370           0.027069\n",
      "0.190000 5.113295 5.084916           0.028380\n",
      "0.200000 5.347106 5.317445           0.029661\n",
      "0.210000 5.575640 5.544728           0.030912\n",
      "0.220000 5.798672 5.766540           0.032132\n",
      "0.230000 6.015981 5.982663           0.033318\n",
      "0.240000 6.227353 6.192883           0.034470\n",
      "0.250000 6.432579 6.396992           0.035587\n",
      "0.260000 6.631457 6.594789           0.036668\n",
      "0.270000 6.823791 6.786079           0.037711\n",
      "0.280000 7.009390 6.970674           0.038717\n",
      "0.290000 7.188072 7.148390           0.039682\n",
      "0.300000 7.359660 7.319052           0.040608\n",
      "0.310000 7.523986 7.482493           0.041493\n",
      "0.320000 7.680885 7.638550           0.042336\n",
      "0.330000 7.830205 7.787069           0.043136\n",
      "0.340000 7.971797 7.927904           0.043893\n",
      "0.350000 8.105522 8.060917           0.044606\n",
      "0.360000 8.231248 8.185974           0.045274\n",
      "0.370000 8.348851 8.302954           0.045897\n",
      "0.380000 8.458214 8.411741           0.046473\n",
      "0.390000 8.559231 8.512227           0.047004\n",
      "0.400000 8.651800 8.604312           0.047487\n",
      "0.410000 8.735831 8.687907           0.047923\n",
      "0.420000 8.811240 8.762929           0.048312\n",
      "0.430000 8.877954 8.829302           0.048652\n",
      "0.440000 8.935907 8.886963           0.048944\n",
      "0.450000 8.985041 8.935853           0.049187\n",
      "0.460000 9.025308 8.975926           0.049382\n",
      "0.470000 9.056668 9.007140           0.049528\n",
      "0.480000 9.079090 9.029465           0.049625\n",
      "0.490000 9.092552 9.042880           0.049672\n",
      "0.500000 9.097041 9.047370           0.049671\n",
      "0.510000 9.092552 9.042931           0.049620\n",
      "0.520000 9.079090 9.029569           0.049521\n",
      "0.530000 9.056668 9.007295           0.049373\n",
      "0.540000 9.025308 8.976131           0.049176\n",
      "0.550000 8.985041 8.936110           0.048931\n",
      "0.560000 8.935907 8.887269           0.048638\n",
      "0.570000 8.877954 8.829657           0.048297\n",
      "0.580000 8.811240 8.763331           0.047909\n",
      "0.590000 8.735831 8.688356           0.047475\n",
      "0.600000 8.651800 8.604806           0.046993\n",
      "0.610000 8.559231 8.512764           0.046466\n",
      "0.620000 8.458214 8.412321           0.045894\n",
      "0.630000 8.348851 8.303575           0.045276\n",
      "0.640000 8.231248 8.186633           0.044615\n",
      "0.650000 8.105522 8.061612           0.043911\n",
      "0.660000 7.971797 7.928634           0.043163\n",
      "0.670000 7.830205 7.787831           0.042374\n",
      "0.680000 7.680885 7.639341           0.041544\n",
      "0.690000 7.523986 7.483311           0.040674\n",
      "0.700000 7.359660 7.319895           0.039765\n",
      "0.710000 7.188072 7.149255           0.038817\n",
      "0.720000 7.009390 6.971558           0.037832\n",
      "0.730000 6.823791 6.786980           0.036811\n",
      "0.740000 6.631457 6.595703           0.035754\n",
      "0.750000 6.432579 6.397915           0.034664\n",
      "0.760000 6.227353 6.193813           0.033540\n",
      "0.770000 6.015981 5.983597           0.032384\n",
      "0.780000 5.798672 5.767474           0.031198\n",
      "0.790000 5.575640 5.545659           0.029982\n",
      "0.800000 5.347106 5.318369           0.028737\n",
      "0.810000 5.113295 5.085829           0.027466\n",
      "0.820000 4.874438 4.848269           0.026169\n",
      "0.830000 4.630770 4.605923           0.024847\n",
      "0.840000 4.382533 4.359030           0.023502\n",
      "0.850000 4.129970 4.107834           0.022136\n",
      "0.860000 3.873331 3.852582           0.020749\n",
      "0.870000 3.612870 3.593527           0.019343\n",
      "0.880000 3.348844 3.330924           0.017920\n",
      "0.890000 3.081513 3.065032           0.016481\n",
      "0.900000 2.811140 2.796114           0.015026\n",
      "0.910000 2.537993 2.524435           0.013559\n",
      "0.920000 2.262342 2.250262           0.012080\n",
      "0.930000 1.984458 1.973868           0.010590\n",
      "0.940000 1.704615 1.695524           0.009092\n",
      "0.950000 1.423091 1.415505           0.007586\n",
      "0.960000 1.140162 1.134087           0.006074\n",
      "0.970000 0.856107 0.851549           0.004559\n",
      "0.980000 0.571208 0.568168           0.003040\n",
      "0.990000 0.285745 0.284225           0.001520\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.98\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.294905 0.293837           0.001068\n",
      "0.020000 0.589519 0.587385           0.002134\n",
      "0.030000 0.883551 0.880354           0.003197\n",
      "0.040000 1.176711 1.172456           0.004255\n",
      "0.050000 1.468710 1.463402           0.005308\n",
      "0.060000 1.759260 1.752905           0.006355\n",
      "0.070000 2.048073 2.040679           0.007394\n",
      "0.080000 2.334865 2.326440           0.008425\n",
      "0.090000 2.619353 2.609907           0.009446\n",
      "0.100000 2.901256 2.890799           0.010457\n",
      "0.110000 3.180296 3.168839           0.011457\n",
      "0.120000 3.456197 3.443753           0.012444\n",
      "0.130000 3.728687 3.715269           0.013417\n",
      "0.140000 3.997497 3.983121           0.014377\n",
      "0.150000 4.262363 4.247042           0.015321\n",
      "0.160000 4.523022 4.506773           0.016249\n",
      "0.170000 4.779217 4.762057           0.017160\n",
      "0.180000 5.030696 5.012643           0.018054\n",
      "0.190000 5.277210 5.258282           0.018928\n",
      "0.200000 5.518516 5.498734           0.019783\n",
      "0.210000 5.754377 5.733759           0.020617\n",
      "0.220000 5.984558 5.963127           0.021431\n",
      "0.230000 6.208833 6.186611           0.022222\n",
      "0.240000 6.426981 6.403990           0.022990\n",
      "0.250000 6.638786 6.615051           0.023735\n",
      "0.260000 6.844039 6.819583           0.024456\n",
      "0.270000 7.042539 7.017387           0.025152\n",
      "0.280000 7.234088 7.208265           0.025822\n",
      "0.290000 7.418498 7.392031           0.026467\n",
      "0.300000 7.595586 7.568502           0.027084\n",
      "0.310000 7.765179 7.737505           0.027674\n",
      "0.320000 7.927109 7.898872           0.028236\n",
      "0.330000 8.081215 8.052445           0.028770\n",
      "0.340000 8.227346 8.198072           0.029275\n",
      "0.350000 8.365358 8.335608           0.029750\n",
      "0.360000 8.495114 8.464919           0.030196\n",
      "0.370000 8.616487 8.585876           0.030611\n",
      "0.380000 8.729356 8.698360           0.030996\n",
      "0.390000 8.833611 8.802261           0.031350\n",
      "0.400000 8.929147 8.897475           0.031672\n",
      "0.410000 9.015872 8.983909           0.031963\n",
      "0.420000 9.093699 9.061477           0.032222\n",
      "0.430000 9.162552 9.130103           0.032449\n",
      "0.440000 9.222362 9.189718           0.032644\n",
      "0.450000 9.273071 9.240265           0.032806\n",
      "0.460000 9.314629 9.281693           0.032936\n",
      "0.470000 9.346994 9.313961           0.033033\n",
      "0.480000 9.370135 9.337037           0.033097\n",
      "0.490000 9.384028 9.350899           0.033129\n",
      "0.500000 9.388661 9.355533           0.033128\n",
      "0.510000 9.384028 9.350934           0.033095\n",
      "0.520000 9.370135 9.337106           0.033028\n",
      "0.530000 9.346994 9.314064           0.032930\n",
      "0.540000 9.314629 9.281830           0.032798\n",
      "0.550000 9.273071 9.240436           0.032635\n",
      "0.560000 9.222362 9.189922           0.032440\n",
      "0.570000 9.162552 9.130339           0.032212\n",
      "0.580000 9.093699 9.061745           0.031954\n",
      "0.590000 9.015872 8.984208           0.031664\n",
      "0.600000 8.929147 8.897805           0.031343\n",
      "0.610000 8.833611 8.802620           0.030991\n",
      "0.620000 8.729356 8.698747           0.030609\n",
      "0.630000 8.616487 8.586290           0.030197\n",
      "0.640000 8.495114 8.465358           0.029756\n",
      "0.650000 8.365358 8.336072           0.029287\n",
      "0.660000 8.227346 8.198558           0.028788\n",
      "0.670000 8.081215 8.052953           0.028262\n",
      "0.680000 7.927109 7.899400           0.027708\n",
      "0.690000 7.765179 7.738051           0.027128\n",
      "0.700000 7.595586 7.569065           0.026521\n",
      "0.710000 7.418498 7.392608           0.025889\n",
      "0.720000 7.234088 7.208855           0.025232\n",
      "0.730000 7.042539 7.017987           0.024551\n",
      "0.740000 6.844039 6.820193           0.023847\n",
      "0.750000 6.638786 6.615667           0.023119\n",
      "0.760000 6.426981 6.404611           0.022370\n",
      "0.770000 6.208833 6.187234           0.021599\n",
      "0.780000 5.984558 5.963750           0.020807\n",
      "0.790000 5.754377 5.734380           0.019996\n",
      "0.800000 5.518516 5.499350           0.019166\n",
      "0.810000 5.277210 5.258892           0.018319\n",
      "0.820000 5.030696 5.013243           0.017453\n",
      "0.830000 4.779217 4.762645           0.016572\n",
      "0.840000 4.523022 4.507347           0.015675\n",
      "0.850000 4.262363 4.247599           0.014764\n",
      "0.860000 3.997497 3.983659           0.013839\n",
      "0.870000 3.728687 3.715786           0.012901\n",
      "0.880000 3.456197 3.444245           0.011952\n",
      "0.890000 3.180296 3.169304           0.010992\n",
      "0.900000 2.901256 2.891234           0.010022\n",
      "0.910000 2.619353 2.610310           0.009043\n",
      "0.920000 2.334865 2.326809           0.008057\n",
      "0.930000 2.048073 2.041010           0.007063\n",
      "0.940000 1.759260 1.753196           0.006064\n",
      "0.950000 1.468710 1.463651           0.005059\n",
      "0.960000 1.176711 1.172660           0.004051\n",
      "0.970000 0.883551 0.880511           0.003040\n",
      "0.980000 0.589519 0.587491           0.002027\n",
      "0.990000 0.294905 0.293891           0.001014\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 0.99\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.304356 0.303822           0.000534\n",
      "0.020000 0.608412 0.607345           0.001067\n",
      "0.030000 0.911867 0.910269           0.001599\n",
      "0.040000 1.214422 1.212295           0.002128\n",
      "0.050000 1.515779 1.513125           0.002654\n",
      "0.060000 1.815640 1.812463           0.003178\n",
      "0.070000 2.113710 2.110012           0.003697\n",
      "0.080000 2.409693 2.405480           0.004213\n",
      "0.090000 2.703298 2.698575           0.004723\n",
      "0.100000 2.994235 2.989006           0.005229\n",
      "0.110000 3.282218 3.276489           0.005728\n",
      "0.120000 3.566961 3.560739           0.006222\n",
      "0.130000 3.848184 3.841475           0.006709\n",
      "0.140000 4.125609 4.118420           0.007189\n",
      "0.150000 4.398963 4.391302           0.007661\n",
      "0.160000 4.667976 4.659851           0.008125\n",
      "0.170000 4.932381 4.923801           0.008580\n",
      "0.180000 5.191920 5.182893           0.009027\n",
      "0.190000 5.446334 5.436870           0.009464\n",
      "0.200000 5.695374 5.685482           0.009892\n",
      "0.210000 5.938793 5.928484           0.010309\n",
      "0.220000 6.176351 6.165635           0.010716\n",
      "0.230000 6.407813 6.396702           0.011111\n",
      "0.240000 6.632952 6.621457           0.011495\n",
      "0.250000 6.851545 6.839678           0.011868\n",
      "0.260000 7.063377 7.051149           0.012228\n",
      "0.270000 7.268238 7.255661           0.012576\n",
      "0.280000 7.465925 7.453014           0.012911\n",
      "0.290000 7.656245 7.643012           0.013234\n",
      "0.300000 7.839009 7.825467           0.013542\n",
      "0.310000 8.014037 8.000200           0.013837\n",
      "0.320000 8.181156 8.167038           0.014118\n",
      "0.330000 8.340202 8.325816           0.014385\n",
      "0.340000 8.491016 8.476378           0.014638\n",
      "0.350000 8.633451 8.618576           0.014875\n",
      "0.360000 8.767366 8.752267           0.015098\n",
      "0.370000 8.892628 8.877322           0.015306\n",
      "0.380000 9.009114 8.993616           0.015498\n",
      "0.390000 9.116710 9.101035           0.015675\n",
      "0.400000 9.215308 9.199472           0.015836\n",
      "0.410000 9.304812 9.288830           0.015982\n",
      "0.420000 9.385134 9.369022           0.016111\n",
      "0.430000 9.456193 9.439968           0.016225\n",
      "0.440000 9.517920 9.501598           0.016322\n",
      "0.450000 9.570254 9.553851           0.016403\n",
      "0.460000 9.613144 9.596675           0.016468\n",
      "0.470000 9.646546 9.630029           0.016517\n",
      "0.480000 9.670428 9.653879           0.016549\n",
      "0.490000 9.684767 9.668202           0.016565\n",
      "0.500000 9.689549 9.672984           0.016564\n",
      "0.510000 9.684767 9.668220           0.016548\n",
      "0.520000 9.670428 9.653914           0.016515\n",
      "0.530000 9.646546 9.630081           0.016465\n",
      "0.540000 9.613144 9.596744           0.016400\n",
      "0.550000 9.570254 9.553936           0.016318\n",
      "0.560000 9.517920 9.501700           0.016220\n",
      "0.570000 9.456193 9.440086           0.016106\n",
      "0.580000 9.385134 9.369156           0.015977\n",
      "0.590000 9.304812 9.288980           0.015832\n",
      "0.600000 9.215308 9.199637           0.015672\n",
      "0.610000 9.116710 9.101214           0.015496\n",
      "0.620000 9.009114 8.993810           0.015305\n",
      "0.630000 8.892628 8.877529           0.015099\n",
      "0.640000 8.767366 8.752487           0.014878\n",
      "0.650000 8.633451 8.618807           0.014644\n",
      "0.660000 8.491016 8.476622           0.014394\n",
      "0.670000 8.340202 8.326070           0.014131\n",
      "0.680000 8.181156 8.167302           0.013854\n",
      "0.690000 8.014037 8.000473           0.013564\n",
      "0.700000 7.839009 7.825748           0.013261\n",
      "0.710000 7.656245 7.643300           0.012945\n",
      "0.720000 7.465925 7.453309           0.012616\n",
      "0.730000 7.268238 7.255962           0.012276\n",
      "0.740000 7.063377 7.051453           0.011923\n",
      "0.750000 6.851545 6.839986           0.011560\n",
      "0.760000 6.632952 6.621767           0.011185\n",
      "0.770000 6.407813 6.397014           0.010800\n",
      "0.780000 6.176351 6.165947           0.010404\n",
      "0.790000 5.938793 5.928794           0.009998\n",
      "0.800000 5.695374 5.685790           0.009583\n",
      "0.810000 5.446334 5.437175           0.009159\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.820000 5.191920 5.183193           0.008727\n",
      "0.830000 4.932381 4.924095           0.008286\n",
      "0.840000 4.667976 4.660138           0.007838\n",
      "0.850000 4.398963 4.391581           0.007382\n",
      "0.860000 4.125609 4.118690           0.006920\n",
      "0.870000 3.848184 3.841733           0.006451\n",
      "0.880000 3.566961 3.560985           0.005976\n",
      "0.890000 3.282218 3.276722           0.005496\n",
      "0.900000 2.994235 2.989224           0.005011\n",
      "0.910000 2.703298 2.698776           0.004522\n",
      "0.920000 2.409693 2.405664           0.004028\n",
      "0.930000 2.113710 2.110178           0.003532\n",
      "0.940000 1.815640 1.812608           0.003032\n",
      "0.950000 1.515779 1.513250           0.002530\n",
      "0.960000 1.214422 1.212397           0.002026\n",
      "0.970000 0.911867 0.910347           0.001520\n",
      "0.980000 0.608412 0.607398           0.001014\n",
      "0.990000 0.304356 0.303849           0.000507\n",
      "1.000000 -0.000000 0.000000           0.000000\n",
      "y = 1.0\n",
      "x \t u_exact \t u_num \t difference\n",
      "0.000000 0.000000 0.000000           0.000000\n",
      "0.010000 0.314108 0.314108           0.000000\n",
      "0.020000 0.627905 0.627905           0.000000\n",
      "0.030000 0.941083 0.941083           0.000000\n",
      "0.040000 1.253332 1.253332           0.000000\n",
      "0.050000 1.564345 1.564345           0.000000\n",
      "0.060000 1.873813 1.873813           0.000000\n",
      "0.070000 2.181432 2.181432           0.000000\n",
      "0.080000 2.486899 2.486899           0.000000\n",
      "0.090000 2.789911 2.789911           0.000000\n",
      "0.100000 3.090170 3.090170           0.000000\n",
      "0.110000 3.387379 3.387379           0.000000\n",
      "0.120000 3.681246 3.681246           0.000000\n",
      "0.130000 3.971479 3.971479           0.000000\n",
      "0.140000 4.257793 4.257793           0.000000\n",
      "0.150000 4.539905 4.539905           0.000000\n",
      "0.160000 4.817537 4.817537           0.000000\n",
      "0.170000 5.090414 5.090414           0.000000\n",
      "0.180000 5.358268 5.358268           0.000000\n",
      "0.190000 5.620834 5.620834           0.000000\n",
      "0.200000 5.877853 5.877853           0.000000\n",
      "0.210000 6.129071 6.129071           0.000000\n",
      "0.220000 6.374240 6.374240           0.000000\n",
      "0.230000 6.613119 6.613119           0.000000\n",
      "0.240000 6.845471 6.845471           0.000000\n",
      "0.250000 7.071068 7.071068           0.000000\n",
      "0.260000 7.289686 7.289686           0.000000\n",
      "0.270000 7.501111 7.501111           0.000000\n",
      "0.280000 7.705132 7.705132           0.000000\n",
      "0.290000 7.901550 7.901550           0.000000\n",
      "0.300000 8.090170 8.090170           0.000000\n",
      "0.310000 8.270806 8.270806           0.000000\n",
      "0.320000 8.443279 8.443279           0.000000\n",
      "0.330000 8.607420 8.607420           0.000000\n",
      "0.340000 8.763067 8.763067           0.000000\n",
      "0.350000 8.910065 8.910065           0.000000\n",
      "0.360000 9.048271 9.048271           0.000000\n",
      "0.370000 9.177546 9.177546           0.000000\n",
      "0.380000 9.297765 9.297765           0.000000\n",
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa4b8590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def main():\n",
    "    import numpy as np\n",
    "    import seaborn as sns\n",
    "    from numpy import sin , pi, sinh\n",
    "    import matplotlib.pyplot as plt\n",
    "    from mpl_toolkits import mplot3d\n",
    "    global A,B,C,D,E,U,U1,n,m,p,p1,h,k\n",
    "    n=100\n",
    "    m=100\n",
    "    p=3\n",
    "    h=1.0/n\n",
    "    k=1.0/m\n",
    "    x0=0\n",
    "    y0=0\n",
    "    p1=10000\n",
    "    p2=10\n",
    "    eps=0.001\n",
    "    R=np.zeros(p1)\n",
    "    R1=np.zeros(p1)\n",
    "    A=np.zeros((n,m))\n",
    "    B=np.zeros((n,m))\n",
    "    C=np.zeros((n,m))\n",
    "    D=np.zeros((n,m))\n",
    "    E=np.zeros((n,m))\n",
    "    U=np.zeros((n+1,m+1))\n",
    "    x=np.zeros(n+1)\n",
    "    y=np.zeros(m+1)\n",
    "    U1=np.zeros((n+1,m+1))\n",
    "    uexact=np.zeros((n+1,m+1))\n",
    "    x[0]=x0\n",
    "    for i in range(1,n+1):\n",
    "        x[i]=x[i-1]+h\n",
    "    #print(\"x=\",x)\n",
    "    y[0]=y0\n",
    "    for j in range(1,m+1):\n",
    "        y[j]=y[j-1]+k\n",
    "    #print(\"y=\",y)\n",
    "    \n",
    "    for i in range(0,n+1):\n",
    "        U[i,0]=0\n",
    "        U[i,m]=10*sin(pi*x[i])\n",
    "    for j in range(0,m+1):\n",
    "        U[0,j]=0\n",
    "        U[n,j]=0\n",
    "    coeff()\n",
    "    for k1 in range(0,p1):\n",
    "        for i in range(0,n+1):\n",
    "            for j in range(0,m+1):\n",
    "                U1[i,j]=U[i,j]\n",
    "        gauss()\n",
    "        max1=0\n",
    "        flag=0\n",
    "        for i in range(1,n):\n",
    "            for j in range(1,m):\n",
    "                max2=abs(U[i,j]-U1[i,j])\n",
    "                if(max2>max1):\n",
    "                    max1=max2\n",
    "                #print(max1)\n",
    "        R[k1]=max1\n",
    "        R1[k1]=k1+1\n",
    "        if(max1<eps):\n",
    "            flag=1\n",
    "            break\n",
    "    print(\"max1=\",max1)\n",
    "    print(U)\n",
    "    print(\"iterations=\",k1)\n",
    "    plt.figure(figsize=(8,8))\n",
    "    plt.plot(R1[0:k1],R[0:k1],color=\"red\")\n",
    "    plt.xlabel(\"iterations\")\n",
    "    plt.ylabel(\"residue\")\n",
    "    plt.ylim([-0.04,5])\n",
    "    plt.xlim([-0.1,550])\n",
    "    plt.title(\"gauss siedal 60x60\")\n",
    "    plt.show()\n",
    "    if flag==1:\n",
    "        print(\"solution converge \")\n",
    "    else:\n",
    "        print(\"solution diverges\")\n",
    "    for j in range(0,m+1):\n",
    "        t=(j*k)\n",
    "        print ('y =',t)\n",
    "        print(\"x \\t u_exact \\t u_num \\t difference\")\n",
    "        for i in range(0,n+1):\n",
    "            uexact[i,j]=(10/sinh(pi))*sin(pi*x[i])*sinh(pi*y[j])\n",
    "            difference=abs(uexact[i,j]-U[i,j])\n",
    "            print('{0:2f} {1:4f} {2:6f} {3:18f}'.format(x[i],uexact[i,j],U[i,j],difference))\n",
    "    for j in range(0,m+1):\n",
    "        for i in range(0,n+1):\n",
    "            if(j==1.0):\n",
    "                plt.scatter(x[i],U[i,j])\n",
    "                plt.scatter(x[i],uexact[i,j])\n",
    "                #plt.ylim([-5,9.8])\n",
    "                plt.xlim([0,1.1])\n",
    "    plt.show()\n",
    "main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}