This is a GUI which performs numerical differentiation of a function over a number of equaly spaced points. Also with it is a code that grants the coefficients used for numerical differentiation.
The pictures and example should be more than enough for understanding how to use the file.
-1.5 2 -0.5 % Forward
-0.5 -0 0.5 % Central
0.5 -2 1.5 % Backward
% The result is a matrix consisting of coefficients that can be
% used to numerically differentiate, like this:
s = ( d(1,1)*f(x) + d(1,2)*f(x+h) + d(1,3)*f(x+2*h) )/h^Order
s = ( d(2,1)*f(x-h) + d(2,2)*f(x) + d(2,3)*f(x+h) )/h^Order
s = ( d(3,1)*f(x-2*h) + d(3,2)*f(x-h) + d(3,3)*f(x) )/h^Order
% The true answer is s = -0.84147
The code uses the Symbolic Math Toolbox to obtain the true value (in order to calculate the error). If you don't have the Symbolic Math Toolbox then you won't enjoy this benefit (program still works though).
Husam Aldahiyat (2020). Numerical Differentiation (https://www.mathworks.com/matlabcentral/fileexchange/22807-numerical-differentiation), MATLAB Central File Exchange. Retrieved .
A generalized framework called MaxPol has been recently published and made available here
MaxPol provides a framework to design variety of numerical differentiation kernels with properties like:
(1) Cutoff (lowpass) design with no side-lob artifacts (for noise-robust case)
(2) Arbitrary order of differentiation
(3) Arbitrary polynomial accuracy
(4) Derivative matrix design
(5) 2D Derivative Kernels with Steering moments
(6) Intuitive examples in Signal and Image processing
Symbolic Math Toolbox is now an optional feature
Inspired by: Adaptive Robust Numerical Differentiation