blob: 128bb56103c63eb2c6895a861958a4a46933389d (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu May 8 13:27:05 2025
@author: christian
"""
import numpy as np
import matplotlib.pyplot as plt
# step size
h = 0.1
# define grid
x = np.arange(0, 2*np.pi, h)
# compute function
y = np.cos(x)
# compute vector of forward differences
forward_diff = np.diff(y)/h
# compute corresponding grid
x_diff = x[:-1:]
# compute exact solution
exact_solution = -np.sin(x_diff)
# Plot solution
plt.figure(figsize = (12, 8))
plt.plot(x_diff, forward_diff, '--', \
label = 'Finite difference approximation')
plt.plot(x_diff, exact_solution, \
label = 'Exact solution')
plt.legend()
plt.show()
# Compute max error between
# numerical derivative and exact solution
max_error = max(abs(exact_solution - forward_diff))
print(max_error)
|
