Copyright (C) 2020 Andreas Kloeckner
from math import sin, cos
Here are a function and its derivative. We also choose a "center" about which we carry out our experiments:
f = sin
df = cos
x = 2.3
We then compare the accuracy of:
against true
, the actual derivative
for k in range(3, 10):
h = 2**(-k)
fd1 = (f(x+2*h) - f(x))/(2*h)
fd2 = (f(x+h) - f(x))/h
richardson = (-1)*fd1 + 2*fd2
true = df(x)
print("Err FD1: %g\tErr FD: %g\tErr Rich: %g" % (
abs(true-fd1),
abs(true-fd2),
abs(true-richardson)))
Err FD1: 0.08581 Err FD: 0.0448122 Err Rich: 0.00381441 Err FD1: 0.0448122 Err FD: 0.022862 Err Rich: 0.000911846 Err FD1: 0.022862 Err FD: 0.0115423 Err Rich: 0.000222501 Err FD1: 0.0115423 Err FD: 0.00579859 Err Rich: 5.49282e-05 Err FD1: 0.00579859 Err FD: 0.00290612 Err Rich: 1.3644e-05 Err FD1: 0.00290612 Err FD: 0.00145476 Err Rich: 3.39995e-06 Err FD1: 0.00145476 Err FD: 0.000727804 Err Rich: 8.48602e-07