Taylor series forward, backward and central difference using MATLAB

The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point.

clear all
close all
clc

% Defining the function

poly_p = [3 5 7];

% Derivating the function theoritically

p_der = polyder(poly_p);
p_der_eval = polyval(p_der,0);

% Finite difference method - Forward difference method

x_0 = 0;
h   = 0.1;

derivative_forward_difference_first_derivative = (polyval(poly_p, x_0+h) - polyval(poly_p,x_0))/h


% Finite difference method - Backward difference method

x_0 = 0;
h   = 0.2;

derivative_backward_difference_first_derivative = (polyval(poly_p,x_0) - polyval(poly_p,x_0-h))/h


% Finite difference method - Central difference method

x_0 = 0;
h   = 0.2;

derivative_central_difference_first_derivative = (polyval(poly_p,x_0+h) - polyval(poly_p,x_0-h))/(2*h)

Results

poly_p =

     3     5     7


p_der =

     6     5


p_der_eval =

     5


derivative_forward_difference_first_derivative =

    5.3000


derivative_backward_difference_first_derivative =

    4.4000


derivative_central_difference_first_derivative =

    5.0000