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Legandre Numerical solution of nonlinear equations with one unknown
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‎Numerical solution of nonlinear equations with one unknown/Newton's method/2021-09-23_20-01-36.png‎

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‎Numerical solution of nonlinear equations with one unknown/Newton's method/2021-09-23_20-01-47.png‎

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‎Numerical solution of nonlinear equations with one unknown/Newton's method/Newton's method/Newton's method.cpp‎

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// Newton's method.cpp : Этот файл содержит функцию "main". Здесь начинается и заканчивается выполнение программы.
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//
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#include <iostream>
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#include <cmath>
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#include <iomanip>
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using namespace std;
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double function(double);
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double derivative_first(double(double), double);
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/*double derivative_second(double(double), double);*/
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int main()
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{
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//Distance
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double a = 0, b = 0;
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cout << " Input a: "; cin >> a;
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cout << " Input b: "; cin >> b;
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cout << " Distance: [" << a << " , " << b << "]" << endl;
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double x0 = 0.0; // начальное приближение
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cout << " Initial value x0 in [a,b] : "; cin >> x0;
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if (x0<a || x0>b)
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{
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while (x0 < a || x0 > b)
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{
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cout << " !!! x !>b | x!<a. Input x0 in [a,b] : ";
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cin >> x0;
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}
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}
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/*if (function(a) * derivative_second(function, a) > 0 || function(a) * derivative_second(function, a) < 0)
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x0 = a;
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else
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if (function(b) * derivative_second(function, b) > 0 || function(b) * derivative_second(function, b) < 0)
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x0 = b;
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if (x0 == a)
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cout << " x0 = a: " << x0 << endl;
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else
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if(x0==b)
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cout << " x0 = b: " << x0 << endl;
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else
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{
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cout << " x0 = inf";
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return 0;
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}*/
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//y=f(x0)+f'(x0)(x-x0)
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double x = 0;
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int iter = 0;
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cout << " Epsilon : " << DBL_EPSILON << endl;
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for(;;)
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{
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double F = function(x0);
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double F1 = derivative_first(function,x0);
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x = x0 - F / F1;
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cout << "Iteration : " << iter << " F = " << F << setprecision(5) << ";" << setprecision(5) <<" F1 = " << F1 << ";" << setprecision(5) << " x = " << x << endl;
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if (abs(x - x0) < DBL_EPSILON)
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break;
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else
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x0 = x;
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iter++;
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if (iter > 1000)
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{
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cout << " Count iteration very much. The initial value(x0) is not selected correctly. Return programm...";
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return 0;
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}
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}
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cout << endl;
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cout << " Count iteration : " << iter << "; root x = " << x << setprecision(5) << "; f(x) = " << function(x) << setprecision(5);
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cout << endl;
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return 0;
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}
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double function(double x)
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{
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return x*x*x+3*x*x-3; //[0.5,1.5]
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}
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double derivative_first(double func(double), double x)
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{
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const double dx = 1e-10;
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return (function(x + dx) - function(x)) / dx;
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}
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/*double derivative_second(double func(double), double x)
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{
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const double dx = 1e-10;
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return ((function(x + dx) - function((x + dx) + dx)) / ((x + dx) - ((x + dx) + dx)) - (function(x) - function(x + dx)) / (x - (x + dx)))/dx;
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}
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/*double derivative_second(double derivative_first(double,double), double x)
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{
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const double dx = 1e-10;
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double y = x + dx;
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return (derivative_first(function(x),(x + dx)) - derivative_first(function(x), x)) / dx;
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}*/

‎Numerical solution of nonlinear equations with one unknown/Newton's method/Newton's method/Newton's method.sln‎

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Microsoft Visual Studio Solution File, Format Version 12.00
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# Visual Studio Version 16
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VisualStudioVersion = 16.0.28803.202
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MinimumVisualStudioVersion = 10.0.40219.1
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "Newton's method", "Newton's method.vcxproj", "{67C03C6F-7898-43AB-830F-349B3720B0E4}"
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EndProject
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Global
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GlobalSection(SolutionConfigurationPlatforms) = preSolution
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Debug|x64 = Debug|x64
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Debug|x86 = Debug|x86
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Release|x64 = Release|x64
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Release|x86 = Release|x86
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EndGlobalSection
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GlobalSection(ProjectConfigurationPlatforms) = postSolution
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{67C03C6F-7898-43AB-830F-349B3720B0E4}.Debug|x64.ActiveCfg = Debug|x64
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EndGlobalSection
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GlobalSection(SolutionProperties) = preSolution
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HideSolutionNode = FALSE
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EndGlobalSection
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GlobalSection(ExtensibilityGlobals) = postSolution
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SolutionGuid = {57D037DA-8BB5-4242-BBF2-5B6F268027C9}
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EndGlobalSection
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EndGlobal

‎Numerical solution of nonlinear equations with one unknown/Newton's method/Newton's method/Newton's method.vcxproj‎

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‎Numerical solution of nonlinear equations with one unknown/Newton's method/Newton's method/Newton's method.vcxproj.filters‎

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