task6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Задача №6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](images/problem6_1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rk4(ode_function, initial_value, time_step, time_span):\n",
    "    time_points = [0]\n",
    "    values = [initial_value]\n",
    "    num_steps = int(time_span / time_step)\n",
    "    for _ in range(num_steps):\n",
    "        t = time_points[-1]\n",
    "        y = values[-1]\n",
    "        k1 = ode_function(t, y)\n",
    "        k2 = ode_function(t + time_step / 2, y + time_step * k1 / 2)\n",
    "        k3 = ode_function(t + time_step / 2, y + time_step * k2 / 2)\n",
    "        k4 = ode_function(t + time_step, y + time_step * k3)\n",
    "        next_value = y + (time_step / 6) * (k1 + 2 * k2 + 2 * k3 + k4)\n",
    "        time_points.append(t + time_step)\n",
    "        values.append(next_value)\n",
    "    return time_points, values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "bad operand type for unary -: 'list'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[9], line 20\u001b[0m\n\u001b[0;32m     12\u001b[0m \u001b[38;5;66;03m# print(time_points)\u001b[39;00m\n\u001b[0;32m     13\u001b[0m \u001b[38;5;66;03m# print(values)\u001b[39;00m\n\u001b[0;32m     14\u001b[0m \n\u001b[0;32m     15\u001b[0m \u001b[38;5;66;03m# for i in [0.1, 0.01]:\u001b[39;00m\n\u001b[0;32m     16\u001b[0m \u001b[38;5;66;03m#     time_points, values = rk4(f, initial_value, i, 10)\u001b[39;00m\n\u001b[0;32m     17\u001b[0m \u001b[38;5;66;03m#     print(abs(f_actual(time_points[-1]) - values[-1]))\u001b[39;00m\n\u001b[0;32m     19\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(time_points, values, label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mrk4\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m---> 20\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(time_points, \u001b[43mf_actual\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtime_points\u001b[49m\u001b[43m)\u001b[49m, label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mrk4\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m     21\u001b[0m plt\u001b[38;5;241m.\u001b[39mlegend()\n\u001b[0;32m     22\u001b[0m plt\u001b[38;5;241m.\u001b[39mshow()\n",
      "Cell \u001b[1;32mIn[9], line 7\u001b[0m, in \u001b[0;36mf_actual\u001b[1;34m(y)\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mf_actual\u001b[39m(y):\n\u001b[1;32m----> 7\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241;43m-\u001b[39;49m\u001b[43my\u001b[49m) \u001b[38;5;241m*\u001b[39m np\u001b[38;5;241m.\u001b[39mexp(np\u001b[38;5;241m.\u001b[39mlog(initial_value))\n",
      "\u001b[1;31mTypeError\u001b[0m: bad operand type for unary -: 'list'"
     ]
    },
    {
     "data": {
      "image/png": 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jj2nRokUntX/sscd05MgRvfXWW4qLi5Mk5efnn13V/dyUvEGSpJ2HGnWk0au0JKfFFQEA0H+FNEzj9Xq1ceNGFRcXH38Dm03FxcUqLy/v8prnn39eRUVFWrBggbKysjR+/Hjddddd8vm6X2nS0tIij8fT6Ygkg5KcOidzgCRp456jFlcDAED/FlIYqampkc/nU1ZWVqfzWVlZcrvdXV6zc+dOPf300/L5fHrppZe0ZMkS3X///frVr37V7e8pLS1Vampq8MjLywulzH6hYHigd2TDniMWVwIAQP/W56tp/H6/MjMz9eijj2rq1KmaM2eObrvtNq1cubLbaxYvXqy6urrgUVlZ2ddl9rqC/DRJ0obd9IwAAHAqIc0ZycjIkN1uV1VVVafzVVVVys7O7vKanJwcxcXFyW63B8+dd955crvd8nq9cjpPnk/hcrnkcrlCKa3f6egZ+WBfnZpbfYqPs5/mCgAAYlNIPSNOp1NTp05VWVlZ8Jzf71dZWZmKioq6vGbmzJnasWOH/H5/8Nz27duVk5PTZRCJFsPTE5UxwCmvz68P9rM1PAAA3Ql5mKakpESrVq3S448/ri1btujGG29UY2NjcHXN3LlztXjx4mD7G2+8UUeOHNHChQu1fft2vfjii7rrrru0YMGC3vsr+iHDMFQwnKEaAABOJ+SlvXPmzNGhQ4e0dOlSud1uTZ48WWvWrAlOat27d69stuMZJy8vTy+//LJuvvlmTZw4UUOGDNHChQt1yy239N5f0U8V5A/Smo/c2rD7iKRRVpcDAEC/ZJimaVpdxOl4PB6lpqaqrq5OKSkpVpfTYxWVtbp6xT+VmhCn95Z8UTabYXVJAACETU+/v7k3TR86PzdF8XE21R1r1aeHGqwuBwCAfokw0ofi7DZNbr9PzbvMGwEAoEuEkT4WnMTK5mcAAHSJMNLHCvLbd2KlZwQAgC4RRvrYBcMHyTCkvUeaVO1ptrocAAD6HcJIH0uJj9OYrGRJ0gZumgcAwEkII2HAUA0AAN0jjITBtHwmsQIA0B3CSBhMbb9p3kcHPGrytllcDQAA/QthJAyGDExQTmq8fH5TFXtrrS4HAIB+hTASBoZhBIdq3t7FUA0AACcijIRJ0ah0SVL5pzUWVwIAQP9CGAmTGe1h5L29tcwbAQDgBISRMBmWlqghAxPU5je5Tw0AACcgjISJYRgnDNUctrgaAAD6D8JIGBWNZN4IAACfRRgJo46ekQ/218nT3GpxNQAA9A+EkTDKHZigERlJ8pvS+p0s8QUAQCKMhF1H78hbzBsBAEASYSTsOuaNvMW8EQAAJBFGwu5z7WFkq7tehxtaLK4GAADrEUbCbHCyS2OykiVJ77A1PAAAhBErHJ83wlANAACEEQvMYBIrAABBhBELFI5Il2FIOw81qsrTbHU5AABYijBigdTEOI3PTZXE1vAAABBGLDKDeSMAAEgijFimYxLrP3cclmmaFlcDAIB1CCMWmT4iTU67Tftrj+nTQw1WlwMAgGUIIxZJdDpUODJNkvTqtkMWVwMAgHUIIxa6+NzBkqTXthNGAACxizBioUvGZEqS3tl5RE3eNourAQDAGoQRC40anKQhAxPk9flZ4gsAiFmEEQsZhqFLxjBUAwCIbYQRi3UM1by67RBLfAEAMYkwYrEZo9IVZze090iTdtU0Wl0OAABhRxixWJLLoWn5LPEFAMQuwkg/wLwRAEAsI4z0Ax3zRt7eeVjNrT6LqwEAILwII/3A6MwByk2NV0ubX+U7WeILAIgthJF+wDAMXdwxVMO8EQBAjCGM9BMXnxsYqmHeCAAg1hBG+omZ56TLYTO0q6ZRew6zxBcAEDsII/1EcnycCvIHSZLKtlRbXA0AAOFDGOlHis/LkiSt/bjK4koAAAgfwkg/ctm4bEnS+t1HdLTRa3E1AACEB2GkHxmWnqix2cny+U2VbWWoBgAQGwgj/cys8wO9I6985La4EgAAwoMw0s9cdn5g3sjrnxzSMS+7sQIAoh9hpJ8Zl5OiIQMT1Nzq1+ufsOcIACD6EUb6GcMwThiqYVUNACD6EUb6oY6hmrKtVWrz+S2uBgCAvkUY6YcKhg/SoMQ41Ta1av3uI1aXAwBAnyKM9EMOu02Xtm+AxlANACDaEUb6qY55I2s/rpJpmhZXAwBA3yGM9FMXjc5QQpxd+2uP6aMDHqvLAQCgz5xRGFmxYoXy8/MVHx+vwsJCrV+/vkfXPfnkkzIMQ1dfffWZ/NqYEh9n1+fPzZDEBmgAgOgWchhZvXq1SkpKtGzZMm3atEmTJk3SrFmzVF196u3Ld+/erX/7t3/TRRdddMbFxpqOoZo1hBEAQBQLOYw88MADuuGGGzR//nyNGzdOK1euVGJioh577LFur/H5fLruuuv0y1/+UiNHjjyrgmPJpWOzFGc3tL2qQdur6q0uBwCAPhFSGPF6vdq4caOKi4uPv4HNpuLiYpWXl3d73e23367MzEx973vf69HvaWlpkcfj6XTEotTEOF187mBJ0vMVByyuBgCAvhFSGKmpqZHP51NWVlan81lZWXK7ux5KePPNN/X73/9eq1at6vHvKS0tVWpqavDIy8sLpcyoMntSriTp+c0HWFUDAIhKfbqapr6+Xtdff71WrVqljIyMHl+3ePFi1dXVBY/Kyso+rLJ/Kz4vS/FxNu090qT399VZXQ4AAL3OEUrjjIwM2e12VVV13oirqqpK2dnZJ7X/9NNPtXv3bs2ePTt4zu8PbG/ucDi0bds2jRo16qTrXC6XXC5XKKVFrSSXQ8XnZemF9w/q+c0HNClvoNUlAQDQq0LqGXE6nZo6darKysqC5/x+v8rKylRUVHRS+7Fjx+qDDz5QRUVF8Pjyl7+sL3zhC6qoqIjp4ZdQfLl9qOaF9w/I52eoBgAQXULqGZGkkpISzZs3TwUFBZo+fbqWL1+uxsZGzZ8/X5I0d+5cDRkyRKWlpYqPj9f48eM7XT9w4EBJOuk8unfxmMFKiXeoytOid3cf0edGpltdEgAAvSbkMDJnzhwdOnRIS5culdvt1uTJk7VmzZrgpNa9e/fKZmNj197kcth1+fhsPbVhn57ffIAwAgCIKoYZAUs0PB6PUlNTVVdXp5SUFKvLscQbnxzS9b9fr0GJcVp/W7Hi7AQ+AED/1tPvb77RIkTRyHRlDHDqaFOr3vykxupyAADoNYSRCOGw23TVhBxJ0t82swEaACB6EEYiyJcnB1bVvPyRW82tPourAQCgdxBGIsgFwwZpyMAENXp9Ktty6hsTAgAQKQgjEcQwDH2lvXfk6Y2xuystACC6EEYizDcKAhvFvbb9kNx1zRZXAwDA2SOMRJgRGUmanp8mvyn976Z9VpcDAMBZI4xEoG9OC/SOPLWhkjv5AgAiHmEkAl05IVtJTrv2HG7S+l1HrC4HAICzQhiJQIlOh2a33zzvqQ0M1QAAIhthJEJ1TGR96YODqm9utbgaAADOHGEkQl0wbKBGDU7SsVafXnz/oNXlAABwxggjEcowDM05YSIrAACRijASwb46ZajsNkOb9tZqR3W91eUAAHBGCCMRbHCyS/8yNlMSE1kBAJGLMBLhvtk+kfV/N+5TSxs3zwMARB7CSIT7wpjBykmN1+FGr176gImsAIDIQxiJcA67Td/+3HBJ0uNv7bG4GgAAQkcYiQJzpuXJabeporJWmytrrS4HAICQEEaiQMYAl740MUeS9Hj5bmuLAQAgRISRKDFvRr4k6YXNB1XT0GJtMQAAhIAwEiUm5Q3UpLyB8vr8Wv0um6ABACIHYSSKfGdGYCLrn97eozaf3+JqAADoGcJIFLlyQo4yBjh1sK5Zaz+usrocAAB6hDASRVwOu66ZPkyS9Ie3dltbDAAAPUQYiTLXFg6T3WbonV1HtOWgx+pyAAA4LcJIlMlJTdDl52dLkn73xi6LqwEA4PQII1Hohs+PlCT9tWK/9tces7gaAABOjTAShSbnDdSMUelq85v63Rs7rS4HAIBTIoxEqRsvGSVJenJ9pY42ei2uBgCA7hFGotSF52Ro/JAUHWv1sUU8AKBfI4xEKcMwdOPF50gKLPNt8rZZXBEAAF0jjESxy8dnKz89UbVNrXpyPVvEAwD6J8JIFLPbDP3g84G5I797Y6e8bWwRDwDofwgjUe5rFwzR4GSXDtQ16/nNB6wuBwCAkxBGolx8nF3fu3CEJOmRV3fI5zctrggAgM4IIzHgusJhSk2I06eHGvX85v1WlwMAQCeEkRiQHB+nH14c2JV1+f99olYfc0cAAP0HYSRGfGdGvjIGOLXncJOe3rjP6nIAAAgijMSIRKdDP74ksO/Ib8o+UXOrz+KKAAAIIIzEkGsLhyknNV4H65r15/V7rS4HAABJhJGYEh9n10//ZbQkacW6T9mVFQDQLxBGYsw3CoZqWFqiahpa9MfyPVaXAwAAYSTWxNltuqk40Duy8rVP5WlutbgiAECsI4zEoK9MHqJRg5NU29Sq3772qdXlAABiHGEkBtlthm65fKwkadUbu1R5pMniigAAsYwwEqO+OC5LM0aly9vm191rtlpdDgAghhFGYpRhGFrypXGyGdKL7x/U+l1HrC4JABCjCCMx7LycFH1r+jBJ0u0vfCQ/N9EDAFiAMBLjSr54rpJdDn2436OnN7FNPAAg/AgjMS5jgEs/vTSwTfyvX96mhhY2QgMAhBdhBPrOjBHKT0/UofoWPbxuh9XlAABiDGEEcjpsuvXK8yRJv3tjl3ZUN1hcEQAglhBGICmw1PeSMYPl9fl167MfMJkVABA2hBFICiz1veMr45UQZ9f6XUf0l42VVpcEAIgRhBEE5aUl6v+77FxJ0p0vbtGh+haLKwIAxIIzCiMrVqxQfn6+4uPjVVhYqPXr13fbdtWqVbrooos0aNAgDRo0SMXFxadsD2t9Z0a+xg9Jkae5Tbe/8LHV5QAAYkDIYWT16tUqKSnRsmXLtGnTJk2aNEmzZs1SdXV1l+1fffVVXXPNNVq3bp3Ky8uVl5enyy67TPv37z/r4tH7HHab7v7aRNkM6W+bD2jd1q7/fwUAoLcYpmmGNFOxsLBQ06ZN00MPPSRJ8vv9ysvL009/+lMtWrTotNf7fD4NGjRIDz30kObOnduj3+nxeJSamqq6ujqlpKSEUi7O0K9e+Fi/e3OXhgxM0NqSzyvR6bC6JABAhOnp93dIPSNer1cbN25UcXHx8Tew2VRcXKzy8vIevUdTU5NaW1uVlpbWbZuWlhZ5PJ5OB8Lr5i+eqyEDE7S/9pju/js30gMA9J2QwkhNTY18Pp+ysrI6nc/KypLb7e7Re9xyyy3Kzc3tFGg+q7S0VKmpqcEjLy8vlDLRC5JcDt399QmSpD+W79Gr2xiuAQD0jbCuprn77rv15JNP6tlnn1V8fHy37RYvXqy6urrgUVnJMlMrXDR6sL4zI1+S9POn39fRRq+1BQEAolJIYSQjI0N2u11VVVWdzldVVSk7O/uU19533326++679corr2jixImnbOtyuZSSktLpgDUWXTFWowYn6VB9i2599gOFOMUIAIDTCimMOJ1OTZ06VWVlZcFzfr9fZWVlKioq6va6e++9V3fccYfWrFmjgoKCM68WYRcfZ9d/fmuKHDZDf//Qrf/dxCooAEDvCnmYpqSkRKtWrdLjjz+uLVu26MYbb1RjY6Pmz58vSZo7d64WL14cbH/PPfdoyZIleuyxx5Sfny+32y23262GBu5/EinGD0nVzV8MbIb2/z//kSqPNFlcEQAgmoQcRubMmaP77rtPS5cu1eTJk1VRUaE1a9YEJ7Xu3btXBw8eDLZ/5JFH5PV69a//+q/KyckJHvfdd1/v/RXocz+6eJQKhg9SQ0ubSp6qUJvPb3VJAIAoEfI+I1Zgn5H+ofJIk674zzfU0NKmH35+pBa33+kXAICu9Mk+I4hteWmJuvdfA5OPf/v6Tq35sGfLuQEAOBXCCEJy5YQcff/CEZKkn/9ls3bVNFpcEQAg0hFGELJbrhirafmDVN/Sphv/tFHHvD6rSwIARDDCCEIWZ7fpoWsvUMYAl7a663Ub+48AAM4CYQRnJCslXg9eM0U2Q3rmvf36Y/keq0sCAEQowgjOWNGodN1y+VhJ0i//9pHWbeX+NQCA0BFGcFZ+8PmR+sbUofKb0k+e2KQtB7nDMgAgNIQRnBXDMHTnVyeoaGS6Gr0+fe8P76ra02x1WQCACEIYwVlzOmxa+e2pGjk4SQfqmvX9P25ghQ0AoMcII+gVqYlxemzeNA1KjNP7++p00+r32DIeANAjhBH0mvyMJD06t0BOu00vf1Slxc98IL+fJb8AgFMjjKBXTctP02+umSK7zdBfNu7T7S98zB4kAIBTIoyg110+Plv3fj1wD5s/vLVb/7F2u8UVAQD6M8II+sTXpw7V7V85X5L0m3/s0KOvf2pxRQCA/oowgj4ztyhfP581RpJ010tb9fhbu60tCADQLxFG0KcWfOEc/fiSUZKkZc9/pN++Rg8JAKAzwgj63M9njdHP/uUcSVLp37dq+f9tZ1IrACCIMII+ZxiGSi4bo3+/PDBks/z/PtHda7YSSAAAkggjCKMfX3KOls0eJ0n67Ws7tfSvH8nHPiQAEPMIIwir+TNHqPRrE2QY0n+/vUc3/mkjW8cDQIwjjCDsrpk+TA9dc4GcDpte+bhK33q0XIfqW6wuCwBgEcIILHHVxBw98f1CDUqM0+Z9dfrqw//Ujup6q8sCAFiAMALLFOSn6Zkfz9Tw9ETtO3pMX3v4Lb3xySGrywIAhBlhBJYakZGkZ26coQuGDZSnuU3zHluvh1/dwUobAIghhBFYLn2AS0/c8Dl9s2Co/KZ075pt+tGfNqq+udXq0gAAYUAYQb8QH2fXPV+fqLu+OkFxdkMvf1Slr6z4pz6pYh4JAEQ7wgj6DcMwdG3hMD31wyJlp8Rr56FGffmhf+rP6/cybAMAUYwwgn5nyrBBeuFnF2rmOek61urT4mc+0I/+tFFHG71WlwYA6AOEEfRLGQNc+u/vFmrxFWODwzaX/+frevOTGqtLAwD0MsII+i2bzdAPLx6lZ388UyMHJ6nK06Jv//4dLf3rh2poabO6PABALyGMoN8bPyRVL/70Il1XOEyS9MfyPbrsgde0bmu1xZUBAHoDYQQRIcFp151fnaA/fa9QeWkJOlDXrPl/eFcLn3xPhxvYSh4AIhlhBBHlwtEZevmmz+uGi0bIZkh/rTigf7n/NT3+1m61+fxWlwcAOAOGGQFrJj0ej1JTU1VXV6eUlBSry0E/sbmyVoue+UBbDnokSWOykrVs9jjNOCfD4soAAFLPv78JI4hobT6//rx+r+5fu121TYEdWy8/P1uLrxyr4elJFlcHALGNMIKYUtvk1QNrt+tPb++R35QcNkPfnJanhZeOVlZKvNXlAUBMIowgJm11e1T60la9tj1w91+Xw6bvzMjXjy4epUFJTourA4DYQhhBTHtn52Hd+/I2bdxzVJKU5LTr20XD9b0LRygzmZ4SAAgHwghinmmaWretWr9+eXtwkqvTYdM3C4bqh58fpby0RIsrBIDoRhgB2pmmqX9srdZD63bovb21kiS7zdAV47M1f2a+Lhg2SIZhWFskAEQhwgjwGaZp6u2dR/Twqzv0xgn3uJk4NFXfmZGvqybmyOWwW1ghAEQXwghwCh8dqNMf/rlbf918QN62wGZp6UlOfX3qUH2zIE/nZA6wuEIAiHyEEaAHDje06Ml3K/Xf5Xvk9jQHz0/LH6Q504bpivHZSnI5LKwQACIXYQQIQZvPr3XbDmn1u3v1j63V8rf/W5EQZ9cXx2XpK5NzddHowXI6uIMCAPQUYQQ4Q+66Zv3vpn36y4ZK7T7cFDw/MDFOV4zP1uXjc1Q0Mp1gAgCnQRgBzpJpmnp/X52eq9ivv20+qJoT7g6cHO9Q8XlZmnV+ti4ancFQDgB0gTAC9CKf31T5p4f10ocH9cpHVZ2CidNuU+HINF187mB9YWymRmYksVQYAEQYAfqMz2/qvb1HteZDt175uEp7jzR1ej0vLUEzR2VoxjkZmjEqXRkDXBZVCgDWIowAYWCapnbWNGrd1mq9uu2Q3tl1WK2+zv9Kjc1OVuGINBXkp2n6iDRu3AcgZhBGAAs0trRp/a4j+ueOGv3z08PBbehPlJeWoILhaZqcN1CT8wbqvJwUJsMCiEqEEaAfONzQord3HtG7uwPHloOe4LLhDk6HTefnpmjikFSdn5uq84ekaHRmMgEFQMQjjAD9UH1zqzbuOar39taqorJWm/fVqrap9aR2TrtN52QO0NjsZI1pP8ZmpygrxcXkWAARgzACRADTNLXncJM276vVh/vr9OF+jz46UCdPc1uX7ZPjHRo1eIBGDR6gczIHaOTgJI3ISNKwtETFx3FfHQD9C2EEiFCmaaryyDFtcXu0zV2vbe56bXV7tKum8aQhng6GIeWmJmh4eqKGpSUqr/0YlpaooYMSlJ7kpEcFQNgRRoAo09Lm0+6aJu2obtCnhxq0o7pBO2satLumSQ0tXfekdHA5bBoyMEG5AxOUkxqvnNR4ZacmKDvVpayUeGWnxGtQolM2G4EFQO/p6fc320YCEcLlsAfnj5zINE0dbvRqd02jdh9uUuWR9uNokyqPHFNVfbNa2vzaWdOonTWN3b6/w2YoY4BLmSkuZSa7lDHApfQBTqUnBR4zBrg0KNGp9AFODUyMk8vBsBCA3nFGYWTFihX69a9/LbfbrUmTJunBBx/U9OnTu23/l7/8RUuWLNHu3bs1evRo3XPPPbryyivPuGgAxxlGIERkDHCpID/tpNe9bX5VeZq1v/aYDtQe0/6jx+T2NKvK06yDdYHHmgav2vym3J7mTncvPpUBLocGJsYFjgSnUhPjNDAhTqkJcUpJiFNKfOB5cryj/YhTSrxDA+IdSoizM2wEICjkMLJ69WqVlJRo5cqVKiws1PLlyzVr1ixt27ZNmZmZJ7V/6623dM0116i0tFRf+tKX9MQTT+jqq6/Wpk2bNH78+F75IwB0z+mwBeeQdKfV51dNQ4uqPS06VN+i6voWHW5o0eFGr2oaWlTT0KLDDV4dbWrV0SavfH5TDS1tamhp076jx0KuyWYEwswAl0NJwcOuJGfgeaLTrkSnXQnOE57H2ZXQ8RhnlyvOrvg4m+Lj7IHDEXjuctjksLMsGogkIc8ZKSws1LRp0/TQQw9Jkvx+v/Ly8vTTn/5UixYtOqn9nDlz1NjYqBdeeCF47nOf+5wmT56slStX9uh3MmcE6D9M05SnuU1HGr2qbfKq9lhr4LGpVbVNrfI0t6ruWKs8x9rkORb4ub65TfXNrWpoaet2Em5vctgMuRw2ueLsctptcsXZOj3G2W1yOmxyOY4/j7N3HMZJzx12Q3G2wKPDbpPDZshhO/5a4Geb7O3P7R0/247/3PHcZjNkN46fs9sM2Tp+NgwZNgVftwUfRU8SIlKfzBnxer3auHGjFi9eHDxns9lUXFys8vLyLq8pLy9XSUlJp3OzZs3Sc8891+3vaWlpUUvL8RuReTwn72IJwBqGYSi1fThGSgrpWtM01ej1qbG9V6WhOfDY2NKmJq9Pjd42NbX41NDSpmOtPjV5A+ePeX061upTc6tPx1r9avb61NTapuZWv5pbfWpp9cvr8wd/T5vfVJvXp0avr5f/eusYRiCk2AxDNpsCj4YRON8eXDpCi80IvG6o/Wfb8Z87rjnxUTp+nWFIhgLPFbwm8HrH9Qr8L9jWMD77PNBWwTbHzx3PVEbweVfv1d5CwTeSTnhPo9N13b3W+Un7+3V5zclt9JnXOmfBrtt036K7Nqd/n9O9b+C63gmq37twxCl7UPtSSGGkpqZGPp9PWVlZnc5nZWVp69atXV7jdru7bO92u7v9PaWlpfrlL38ZSmkAIoBhGMHhmazTNw+Jz2/K2+ZXS5tPLW3tIaXN3+lcx8+tvsCjty0QYlp9plp9frWe8HObL9Cu1W+qtc2vNn+gTVt72za/KV/7OZ/fVKvflN9vtp8PtPOZZuDxhPM+vym/GajX5w+08fWgu8g0pTbTlGRK0ZOx0I98eXJuZISRcFm8eHGn3hSPx6O8vDwLKwLQ39ltRmBOiTMyV/n4Twgm/uBj4LzfDLxmnhBiJJ3QLvCa3wyc85um/H7JVMf5421MdbxnoKfKVMfrgUeZJ153vE1gQL/juuNtAq8F6uk472/vpOp4rf3Sz1zT0cY84fnxFzq16XiPTtcdd+Jsg44aTmz72fad38c86VxX79ttm5NadNXmzN7npEZdNQn9ki7rkWTpTTxDCiMZGRmy2+2qqqrqdL6qqkrZ2dldXpOdnR1Se0lyuVxyubjtOoDYYbMZsskQG+kiFoU05dzpdGrq1KkqKysLnvP7/SorK1NRUVGX1xQVFXVqL0lr167ttj0AAIgtIQ/TlJSUaN68eSooKND06dO1fPlyNTY2av78+ZKkuXPnasiQISotLZUkLVy4UBdffLHuv/9+XXXVVXryySe1YcMGPfroo737lwAAgIgUchiZM2eODh06pKVLl8rtdmvy5Mlas2ZNcJLq3r17ZbMd73CZMWOGnnjiCf3iF7/QrbfeqtGjR+u5555jjxEAACCJe9MAAIA+0tPvb7YpBAAAliKMAAAASxFGAACApQgjAADAUoQRAABgKcIIAACwFGEEAABYijACAAAsRRgBAACWCnk7eCt0bBLr8XgsrgQAAPRUx/f26TZ7j4gwUl9fL0nKy8uzuBIAABCq+vp6paamdvt6RNybxu/368CBA0pOTpZhGL32vh6PR3l5eaqsrOSeN32Izzl8+KzDg885PPicw6MvP2fTNFVfX6/c3NxON9H9rIjoGbHZbBo6dGifvX9KSgr/oIcBn3P48FmHB59zePA5h0dffc6n6hHpwARWAABgKcIIAACwVEyHEZfLpWXLlsnlclldSlTjcw4fPuvw4HMODz7n8OgPn3NETGAFAADRK6Z7RgAAgPUIIwAAwFKEEQAAYCnCCAAAsFRMh5EVK1YoPz9f8fHxKiws1Pr1660uKaqUlpZq2rRpSk5OVmZmpq6++mpt27bN6rKi3t133y3DMHTTTTdZXUrU2b9/v7797W8rPT1dCQkJmjBhgjZs2GB1WVHH5/NpyZIlGjFihBISEjRq1Cjdcccdp72/CU7t9ddf1+zZs5WbmyvDMPTcc891et00TS1dulQ5OTlKSEhQcXGxPvnkk7DUFrNhZPXq1SopKdGyZcu0adMmTZo0SbNmzVJ1dbXVpUWN1157TQsWLNDbb7+ttWvXqrW1VZdddpkaGxutLi1qvfvuu/rtb3+riRMnWl1K1Dl69KhmzpypuLg4/f3vf9fHH3+s+++/X4MGDbK6tKhzzz336JFHHtFDDz2kLVu26J577tG9996rBx980OrSIlpjY6MmTZqkFStWdPn6vffeq9/85jdauXKl3nnnHSUlJWnWrFlqbm7u++LMGDV9+nRzwYIFwZ99Pp+Zm5trlpaWWlhVdKuurjYlma+99prVpUSl+vp6c/To0ebatWvNiy++2Fy4cKHVJUWVW265xbzwwgutLiMmXHXVVeZ3v/vdTue+9rWvmdddd51FFUUfSeazzz4b/Nnv95vZ2dnmr3/96+C52tpa0+VymX/+85/7vJ6Y7Bnxer3auHGjiouLg+dsNpuKi4tVXl5uYWXRra6uTpKUlpZmcSXRacGCBbrqqqs6/XON3vP888+roKBA3/jGN5SZmakpU6Zo1apVVpcVlWbMmKGysjJt375dkrR582a9+eabuuKKKyyuLHrt2rVLbre7038/UlNTVVhYGJbvxYi4UV5vq6mpkc/nU1ZWVqfzWVlZ2rp1q0VVRTe/36+bbrpJM2fO1Pjx460uJ+o8+eST2rRpk959912rS4laO3fu1COPPKKSkhLdeuutevfdd/Wzn/1MTqdT8+bNs7q8qLJo0SJ5PB6NHTtWdrtdPp9Pd955p6677jqrS4tabrdbkrr8Xux4rS/FZBhB+C1YsEAffvih3nzzTatLiTqVlZVauHCh1q5dq/j4eKvLiVp+v18FBQW66667JElTpkzRhx9+qJUrVxJGetlTTz2l//mf/9ETTzyh888/XxUVFbrpppuUm5vLZx2lYnKYJiMjQ3a7XVVVVZ3OV1VVKTs726KqotdPfvITvfDCC1q3bp2GDh1qdTlRZ+PGjaqurtYFF1wgh8Mhh8Oh1157Tb/5zW/kcDjk8/msLjEq5OTkaNy4cZ3OnXfeedq7d69FFUWvn//851q0aJG+9a1vacKECbr++ut18803q7S01OrSolbHd59V34sxGUacTqemTp2qsrKy4Dm/36+ysjIVFRVZWFl0MU1TP/nJT/Tss8/qH//4h0aMGGF1SVHp0ksv1QcffKCKiorgUVBQoOuuu04VFRWy2+1WlxgVZs6cedLS9O3bt2v48OEWVRS9mpqaZLN1/nqy2+3y+/0WVRT9RowYoezs7E7fix6PR++8805YvhdjdpimpKRE8+bNU0FBgaZPn67ly5ersbFR8+fPt7q0qLFgwQI98cQT+utf/6rk5OTguGNqaqoSEhIsri56JCcnnzQPJykpSenp6czP6UU333yzZsyYobvuukvf/OY3tX79ej366KN69NFHrS4t6syePVt33nmnhg0bpvPPP1/vvfeeHnjgAX33u9+1urSI1tDQoB07dgR/3rVrlyoqKpSWlqZhw4bppptu0q9+9SuNHj1aI0aM0JIlS5Sbm6urr76674vr8/U6/diDDz5oDhs2zHQ6neb06dPNt99+2+qSooqkLo//+q//srq0qMfS3r7xt7/9zRw/frzpcrnMsWPHmo8++qjVJUUlj8djLly40Bw2bJgZHx9vjhw50rztttvMlpYWq0uLaOvWrevyv8nz5s0zTTOwvHfJkiVmVlaW6XK5zEsvvdTctm1bWGozTJMt7QAAgHVics4IAADoPwgjAADAUoQRAABgKcIIAACwFGEEAABYijACAAAsRRgBAACWIowAAABLEUYAAIClCCMAAMBShBEAAGApwggAALDU/wNtS1onjRHRtgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(t, y):\n",
    "    return -y\n",
    "\n",
    "initial_value = 1\n",
    "\n",
    "def f_actual(y):\n",
    "    return np.exp(-y) * np.exp(np.log(initial_value))\n",
    "\n",
    "\n",
    "time_points, values = rk4(f, initial_value, 0.1, 10)\n",
    "\n",
    "# print(time_points)\n",
    "# print(values)\n",
    "\n",
    "# for i in [0.1, 0.01]:\n",
    "#     time_points, values = rk4(f, initial_value, i, 10)\n",
    "#     print(abs(f_actual(time_points[-1]) - values[-1]))\n",
    "\n",
    "plt.plot(time_points, values, label=\"rk4\")\n",
    "plt.plot(time_points, f_actual(time_points), label=\"rk4\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "# plt.plot(time_points, [f_actual(y) for y in time_points], label=\"actual\")\n",
    "f_actual_arr = [f_actual(y) for y in time_points]\n",
    "plt.plot(time_points, [abs(values[i] - f_actual_arr[i])/f_actual_arr[i] for i in range(len(values))], label=\"error\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  }
 ],
 "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": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}