Function taylor4

ode.py:87–127

Calculate the solution of the initial-value problem (IVP). Solve the IVP from the Taylor (Order Four) method. Args: f (function): equation f(x). df1 (function): 1's derivative of equation f(x). df2 (function): 2's derivative of equation f(x). df3 (function):

(f, df1, df2, df3, a, b, n, ya)

def taylor4(f, df1, df2, df3, a, b, n, ya):
    """Calculate the solution of the initial-value problem (IVP).

    Solve the IVP from the Taylor (Order Four) method.

    Args:
        f (function): equation f(x).
        df1 (function): 1's derivative of equation f(x).
        df2 (function): 2's derivative of equation f(x).
        df3 (function): 3's derivative of 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

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

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

    for i in range(0, n):
        y += h * (f(x, y) + 0.5 * h * df1(x, y) + (h ** 2 / 6) * df2(x, y) +
                  (h ** 3 / 24) * df3(x, y))
        x = a + (i + 1) * h

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

    return vx, vy


def rk4(f, a, b, n, ya):