write a function i = csimpson(f,h) that takes as inputs f an array of function values and h the distance between grid values and computes i the composite simpson’s approximation of the integral. in matlab

main.m
function i = csimpson(f, h)
% Input: f - array of function values
%        h - distance between grid values
% Output: i - composite Simpson's approximation of integral

% Check size of f, must have an odd number of elements
if mod(length(f),2) == 0
    error('Length of f must be odd.');
end

% Compute integration limits and midpoints
a = 0;
b = (length(f)-1)*h;
x = linspace(a,b,length(f));

% Composite Simpson's rule
i = (h/3)*(f(1) + 4*sum(f(2:2:end-1)) + 2*sum(f(3:2:end-2)) + f(end));

end
497 chars
20 lines

The function csimpson takes as input an array f of function values and the distance between grid values h, and outputs the composite Simpson's approximation of the integral. It first checks if the length of f is odd, as required by Simpson's rule. It then computes the integration limits using the length of f and the distance between grid values. It applies the composite Simpson's rule formula using array slicing to perform the summations.

gistlibby LogSnag