Runge Kutta Implementation Example

rk_example.py

def runge_kutta(func, x0, y0, x, h=0.5):
    # count number of interation using step size or
    # step height h
    
    n = int((x-x0)/h)
    # iterate for number of iterations
    y = y0
    for i in range(1, n+1):
        # Apply runge-kutta formula to find the value of y
        k1 = h * func(x0, y)
        k2 = h * func(x0 + 0.5*h, y + 0.5*k1)
        k3 = h * func(x0 + 0.5*h, y + 0.5*k2)
        k4 = func(x0 + h, y + h*k3)
        y = y + h*(k1 + 2*k2 + 2*k3 + k4)/6
        
        x0 = x0 + h
    # return y, the result
    return y