Solving for the 1st & 2nd derivatives of a given polynomial using Finite differences methods

finite-differences.py

# -*- coding: utf-8 -*-
"""
Created on Sun Dec 29 16:51:25 2019

@author: DASA0
"""

""" find the 1st & 2nd derivatives of the polynomial at x = 0.1: 
    f(x) = 0.1x^5 -0.2x^3 + 0.1x - 0.2 """
    
f = lambda x: 0.1*x**5 - 0.2*x**3 + 0.1*x - 0.2

h = 0.05
x = 0.1

# Forward differences approximation
dff1 = (f(x+h) - f(x))/h
dff2 = (f(x+2*h) - 2*f(x+h) + f(x))/h**2
print('Solution by forward differences:')
print('f\'(%f) = %f'%(x,dff1))
print('f\'\'(%f) = %f'%(x,dff2))

# Central differences approximation
dfc1 = (f(x+h)-f(x-h))/(2*h)
dfc2 = (f(x+h)-2*f(x)+f(x-h))/h**2
print('\nSolution by central differences:')
print('f\'(%f) = %f'%(x,dfc1))
print('f\'\'(%f) = %f'%(x,dfc2))

# Backward differences approximation
dfb1 = (f(x)-f(x-h))/h
dfb2 = (f(x)-2*f(x-h)+f(x-2*h))/h**2
print('\nSolution by backward differences:')
print('f\'(%f) = %f'%(x,dfb1))
print('f\'\'(%f) = %f'%(x,dfb2))