#!/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)