central finite differencing in matlab in matlab

Central finite differencing is a numerical method for approximating the derivative of a function at a point. In Matlab, it can be implemented using the following code:

main.m
function dfdx = central_diff(f,x,h)
% Central difference formula for approximating derivative
% Input:
%   f   : function handle for f(x)
%   x   : point at which derivative is to be approximated
%   h   : step size
% Output:
%   dfdx: approximated derivative

dfdx = (f(x+h) - f(x-h)) / (2*h);
end
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In this code, the function central_diff takes in a function handle f, a point x, and a step size h as inputs. It then implements the central difference formula to approximate the derivative of f at x. The approximated derivative is returned as the output dfdx.

To use this function, first define the function f that you want to differentiate, for example:

main.m
f = @(x) sin(x);
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You can then call central_diff with appropriate inputs, for example:

main.m
dfdx = central_diff(f,1,0.1);
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This would approximate the derivative of f at x=1 with a step size of h=0.1.