import numpy as np
import matplotlib.pyplot as plt
plt.style.use('seaborn-v0_8-poster')
%matplotlib inline
# step size
h = 0.1
# define grid
x = np.arange(0, 2*np.pi, h) 
# compute function
y = np.sin(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.cos(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)

0.04997515074549317

print(plt.style.available)

['Solarize_Light2', '_classic_test_patch', '_mpl-gallery', '_mpl-gallery-nogrid', 'bmh', 'classic', 'dark_background', 'fast', 'fivethirtyeight', 'ggplot', 'grayscale', 'petroff10', 'seaborn-v0_8', 'seaborn-v0_8-bright', 'seaborn-v0_8-colorblind', 'seaborn-v0_8-dark', 'seaborn-v0_8-dark-palette', 'seaborn-v0_8-darkgrid', 'seaborn-v0_8-deep', 'seaborn-v0_8-muted', 'seaborn-v0_8-notebook', 'seaborn-v0_8-paper', 'seaborn-v0_8-pastel', 'seaborn-v0_8-poster', 'seaborn-v0_8-talk', 'seaborn-v0_8-ticks', 'seaborn-v0_8-white', 'seaborn-v0_8-whitegrid', 'tableau-colorblind10']