ChM_12

#include <iostream>
#include <cmath>

using namespace std;

inline double function(double x, double y)
{
    return x + cos(y/sqrt(5));
}

void Euler(const double x0, const double y0, const double x1, const double h)
{
    double x = x0, y = y0;
    cout << "   Euler's method\nx = " << x << "\t y = " << y << endl;
    while (x <= x1)
    {
        double f = function(x, y); //визначення приросту
        y += h*f;
        x += h;
        cout << "x = " << x << "\t y = " << y << endl;
    }
}

void Runge_Kutta(const double x0, const double y0, const double x1, const double h)
{
    double x = x0, y = y0;
    cout << "\nRunge-Kutta's method\nx = " << x << "\t y = " << y << endl;
    while (x <= x1)
    {
        double k1 = h* function(x,y); //визначення коефіцієнтів
        double k2 = h * function(x+h/2, y+k1/2);
        double k3 = h * function(x+h/2, y+k2/2);
        double k4 = h * function(x+h, y+k3);
        double f = (k1+2*k2+2*k3+k4)/6; //визначення приросту
        y += f;
        x += h;
        cout << "x = " << x << "\t y = " << y << endl;
    }
}

void Adams(const double x0, const double y0, const double x, const double h)
{
    double x4 = x0, y = y0, y4 = y0, x1 = x4+3*h, x2 = x4 + 2 * h, x3 = x4 + h;
    double y3 = y4 + h * function(x4, y4);
    double y2 = y3 + h*(3*function(x3, y3) - function(x4, y4))/2;
    double y1 = y2 + h*(23*function(x2,y2)-16*function(x3, y3) + 5*(x4, y4))/12;
    cout << "\n   Adams method\nx = " << x4 << "\t y = " << y4 << endl;
    cout << "x = " << x3 << "\t y = " << y3 << endl;
    cout << "x = " << x2 << "\t y = " << y2 << endl;
    cout << "x = " << x1 << "\t y = " << y1 << endl;
    while (x1 <= x)
    {
        y = y1 + h*(55*function(x1,y1)-59*function(x2,y2)+37*function(x3,y3)-9*function(x4,y4))/24;
        y4 = y3;
        y3 = y2;
        y2 = y1;
        y1 = y;
        x4 = x3;
        x3 = x2;
        x2 = x1;
        x1 += h;
        cout << "x = " << x1 << "\t y = " << y << endl;
    }
}

int main()
{
    const double x0 = 1.8;
    const double y0 = 2.6;
    const double x1 = 2.8;
    const int    n  = 10;
    const double h  = (x1 - x0) / n;

    Euler(x0, y0, x1, h);
    Runge_Kutta(x0, y0, x1, h);
    Adams(x0, y0, x1, h);

    system("pause");
    return 0;
}