RK_method

#include<stdio.h>

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, k3, k4, k5;

	// Iterate for number of iterations
	float y = y0;
	for (int i = 0; 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);
		k3 = h * dydx(x0 + 0.5*h, y + 0.5*k2);
		k4 = h * dydx(x0 + h, y + k3);

		// Update next value of y
		y = y + (1.0/ 6.0) * (k1 + 2 * k2 + 2 * k3 + k4);;

		// Update next value of x
		x0 = x0 + h;

		printf("k1 = %f, k2 = %f, k3 = %f, k4 = %f\n", k1, k2, k3, k4);
		printf("Updated values of x and y are %f, %f\n\n", x0, y);
	}

	return y;
}

void main()
{
	float x0, y, x, h;
        printf("Enter the values of x0, y, x, h: ");
        scanf("%f %f %f %f", &x0, &y, &x, &h);

        printf("The value of y at x is : %f\n", rungeKutta(x0, y, x, h));
	return;
}