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python finite difference approximation backward difference

import numpy as np

# Define x, y, and derived y
x = np.linspace(0.78, 0.79, 100)
y = np.sin(x)
dy = np.cos(x)

# Init variable to store backward diff calculation
dyb = [0.0] * len(x)
# set first element by forward difference
dyb[0] = (y[0] - y[1]) / (x[0] - x[1])
# Calculate backward diff
for i in range(1,len(y)):
    dyb[i] = (y[i] - y[i-1]) / (x[i]-x[i-1])
    
# Plot result
plt.figure(figsize = (12,8))
plt.plot(x, dy, label='Exact')
plt.plot(x, dyb, '--', label='backward')
plt.legend()
plt.show()

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python finite difference approximation backward difference

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