20. Finite differences in Python

import numpy as np

a = 1

anum = np.int32(1)

b = 0.1

bnum = np.float64(0.1)

c = [1, 2, 3]

cnum = np.array([1, 2, 3])

d = [1.1, 2, 3]

dnum = np.array([1.1, 2, 3])

poly_p = np.array([-4, 7, -3, 9])

p_der = np.polyder(poly_p)

p_der_eval = np.polyval(p_der, 0)

p_der_eval

np.int64(-3)

x_0 = 0

h = np.float64(0.25)

forward_difference = (np.polyval(poly_p, x_0 + h) - np.polyval(poly_p, x_0)) / h

forward_difference

np.float64(-1.5)

backward_difference = (np.polyval(poly_p, x_0) - np.polyval(poly_p, x_0 - h)) / h

backward_difference

np.float64(-5.0)

central_difference = (np.polyval(poly_p, x_0 + h) - np.polyval(poly_p, x_0 - h)) / (
    2 * h
)

central_difference

np.float64(-3.25)