The following is the code for evaluating a definite integral of a given function by a Numerical Method called Simpson’s 1/3rd Rule.

DOWNLOAD:simpson

funcprot(0);
function ans=simpson(a,b,n,g)
    h=(b-a)/n;
    sum=0;
    for i=1:n-1
        x=a+i*h;
        if modulo(i,2)==0
            sum=sum+2*g(x);
        else 
            sum=sum+4*g(x);
        end 
    end
    ans=(h/3)*(g(a)+g(b)+sum);
endfunction

You can either copy the code above and save it as a .sci file or download the file simpson . Once you run the code, the function ‘simpson(a,b,n,f)’ can be called by other programs or even in the console.

Function syntax:

simpson(a,b,n,f)

where,

a=initial limit(real no.)
b=final limit(real no.)
n=no. of sub-intervals(the higher the value of ‘n’ the better is the result.
NOTE: n should be an even no.

Example:
The following code snippet evaluates the integral of x^4 from 0 to 2.

deff('a=f(x)','a=x^4');
integral=simpson(0,2,30,f);

Here is a comparison of the result with the inbuilt function ‘intg’.

Manas Sharma

PhD researcher at Friedrich-Schiller University Jena, Germany. I'm a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT and Machine Learning related apps and softwares from time to time. Can code in most of the popular languages. Like to share my knowledge in Physics and applications using this Blog and a YouTube channel.