compute numerical approximations using center in matlab

To compute numerical approximations using the center method in MATLAB, we first need to define the function we want to approximate. Let's say we have a function y = f(x), and we want to approximate its derivative at some point x0. The center difference approximation for the first derivative is given by:

f'(x0) ≈ (f(x0 + h) - f(x0 - h)) / (2h)

where h is a small step size to approach zero. We can implement this formula in MATLAB as follows:

main.m
function dfdx = center_diff(f, x0, h)
% f is the function handle
% x0 is the point at which to evaluate the derivative
% h is the step size

dfdx = (f(x0 + h) - f(x0 - h)) / (2*h);
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We can then call this function with any suitable function handle and values of x0 and h. For example, if we want to approximate the derivative of the function y = sin(x) at x = 0.5 with a step size of h = 0.01, we can do the following:

main.m
f = @(x) sin(x);  % function handle for y = sin(x)
x0 = 0.5;         % point at which to approximate derivative
h = 0.01;         % step size

dfdx = center_diff(f, x0, h);

disp(dfdx);       % display the approximate derivative
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This will output an approximation of the derivative of sin(x) at x = 0.5 using the center difference method with a step size of 0.01.