How to Make Simpsons Rule UDF

function output = Simpsons(f,a,b,h)

% f - funtion

% a - This is the initial x value

% b - This is the final x value

% h - This is the step-size

x=[a:h:b]; %need to create a vector of n+1 evenly spaced points

sr=(h/3)*(f(x(1))+2*sum(f(x(3:2:end-2)))+4*sum(f(x(2:2:end)))+f(x(end)))

output=sr

end

I made this simpsons rule UDF and it works can someone just explain wihat the last line reads? I don't fully understand it. Also please let me know if this is a valid UDF for Simpsons if you do not see any errors.

Answer 1

[Mohith Kulkarni]

It is a valid simpsons rule implementation. Let me break the line down.

sr=(h/3)*(f(x(1))+2*sum(f(x(3:2:end-2)))+4*sum(f(x(2:2:end)))+f(x(end)))

This expression above is equivalent to (Δx/3)*[f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+⋯+4f(xn−1)+f(xn)].

x(3:2:end-2) %j:i:k creates a regularly-spaced vector using i as the increment between elements.

So here indexing into the elements of x at odd places. We left out the end as f(xn) is multiplied with 1 and not 2. Similarly, access elements of x at even positions using

x(2:2:end)

Since we are passing a vector to f, the ouput is a vector and sum is used to find the sum of the output vector.

sum(f(x(3:2:end-2)))