Function rk4

ode.py:130–173

Calculate the solution of the initial-value problem (IVP). Solve the IVP from the Runge-Kutta (Order Four) method. Args: f (function): equation f(x). a (float): the initial point. b (float): the final point. n (int): number of intervals. ya (numpy.nd

(f, a, b, n, ya)

def rk4(f, a, b, n, ya):
    """Calculate the solution of the initial-value problem (IVP).

    Solve the IVP from the Runge-Kutta (Order Four) method.

    Args:
        f (function): equation f(x).
        a (float): the initial point.
        b (float): the final point.
        n (int): number of intervals.
        ya (numpy.ndarray): initial values.

    Returns:
        vx (numpy.ndarray): x values.
        vy (numpy.ndarray): y values (solution of IVP).
    """
    vx = np.zeros(n)
    vy = np.zeros(n)

    h = (b - a) / n
    x = a
    y = ya

    k = np.zeros(4)

    vx[0] = x
    vy[0] = y

    print(f"i = 000,\tx = {x:+.4f},\ty = {y:+.4f}")

    for i in range(0, n):
        k[0] = h * f(x, y)
        k[1] = h * f(x + h / 2, y + k[0] / 2)
        k[2] = h * f(x + h / 2, y + k[1] / 2)
        k[3] = h * f(x + h, y + k[2])

        x = a + (i + 1) * h
        y += (k[0] + 2 * k[1] + 2 * k[2] + k[3]) / 6

        print(f"i = {(i+1):03d},\tx = {x:+.4f},\ty = {y:+.4f}")
        vx[i] = x
        vy[i] = y

    return vx, vy


def rk4_system(f, a, b, n, ya):