central finite differencing of a multivariate function in matlab

To perform central finite differencing of a multivariate function in MATLAB, you can use the gradient function. This function computes the numerical gradient of a scalar function of several variables using central differences.

Here's an example:

main.m
% Define the function to differentiate
f = @(x,y) x^2 + y^2;

% Define the point at which to compute the gradient
x0 = 1;
y0 = 2;

% Define the step sizes for finite differencing
h = 0.01;

% Compute the gradient using central differences
dfdx = (f(x0+h,y0) - f(x0-h,y0)) / (2*h);
dfdy = (f(x0,y0+h) - f(x0,y0-h)) / (2*h);
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In this example, we defined a simple function f that takes two variables x and y. We then used the gradient function to compute the partial derivatives of f with respect to x and y at the point (x0,y0). Finally, we computed the numerical gradient using the central difference approximation formula.