rk4.py

def runge_kutta_fourth(rhs, h, x, y):
    """
    Solves one step using a fourth-order Runge-Kutta method.

    Moin, Parviz. 2010. Fundamentals of Engineering Numerical Analysis. 2nd ed.
    Cambridge University Press. New York, New York.

    :param rhs: "Right-hand Side" of the equation(s). Everything but the derivative. (e.g dy/dx = f(x))
    :param h: step size
    :param x: step dimension
    :param y: output dimension
    :return:
    """

    k_1 = rhs(x, y)
    k_2 = rhs(x + h / 2.0, y + k_1 / 2.0)
    k_3 = rhs(x + h / 2.0, y + k_2 / 2.0)
    k_4 = rhs(x + h, y + k_3)

    return y + (k_1 + 2 * (k_2 + k_3) + k_4) / 6.0 * h