RK

// C++ program to implement Runge
// Kutta method
#include <bits/stdc++.h>

using namespace std;

// A sample differential equation
// "dy/dx = (x - y)/2"

float dydx(float x, float y)
{

    return (x + y - 2);
}

// Finds value of y for a given x
// using step size h
// and initial value y0 at x0.

float rungeKutta(float x0, float y0,

                 float x, float h)
{

    // Count number of iterations

    // using step size or

    // step height h

    int n = (int)((x - x0) / h);


    float k1, k2;


    // Iterate for number of iterations

    float y = y0;

    for (int i = 1; i <= n; i++)
    {

        // Apply Runge Kutta Formulas

        // to find next value of y

        k1 = h * dydx(x0, y);

        k2 = h * dydx(x0 + 0.5 * h,

                      y + 0.5 * k1);


        // Update next value of y

        y = y + (1.0 / 6.0) * (k1 + 2 * k2);


        // Update next value of x

        x0 = x0 + h;

    }


    return y;
}

// Driver Code

int main()
{

    float x0 = 0, y = 1,

          x = 2, h = 0.2;


    cout << fixed << setprecision(6) << "y(x) = " << rungeKutta(x0, y, x, h);

    return 0;
}