Matlab Function for Composite Simpson

[ver_mathstats]

Homework Statement

We need to evaluate an integral sin(1/x) where b = 1 and a = 0.1 using composite Simpson in Matlab for n = 2, 4, 8... until the absolute error is within 10^-4, then we are required to apply the adaptive Simpson rule and compare the two. The program needs to output the number and error.

Relevant Equations

composite simpson rule

function I=main_simpson(a,b,tol)
f = @(x) sin(1./x);
SO = 0;
N = 10;
S = 1;
while (abs(S-SO)>tol)
    SO = S;
    h = (b-a)/(2*N);
    i = 0:N-1;
    xi = a+2*i*h;
    xi1 = a+2*(i+0.5)*h;
    xi2 = a+2*(i+1)*h;
    S = (h/3)*sum(f(xi)+4*f(xi1)+f(xi2));
    N = 2*N;
end
end

<Moderator's note: please use CODE tags when posting code.>

I keep experiencing errors when trying to use my composite Simpson code, could anyone tell me how I can improve this? The error is always coming from the while loop but I'm really unsure why and I do not know how to proceed or nothing happens when I input data into my function so I am really confused. Any help is appreciated.

 

[Mark44]

S = (h/3)*sum(f(xi)+4*f(xi1)+f(xi2));

Why is "sum" there on the right side of the assignment? Matlab isn't my strong suit, but I believe that sum() is intended to be used on arrays.

The above should be written as S = (h/3) * (f(xi)+4*f(xi1)+f(xi2));, I believe.

I keep experiencing errors when trying to use my composite Simpson code, could anyone tell me how I can improve this? The error is always coming from the while loop but I'm really unsure why and I do not know how to proceed or nothing happens when I input data into my function so I am really confused.

What sort of errors? If you're getting error messages that possibly include the line number where the error occurred, that's useful information that should be included.

 

[DrClaude]

You have

function I=main_simpson(a,b,tol)

So the function will return the value of I, which is not what you calculate. You calculate the integral into S.

Note also that you do not follow what the question asks with regards to the number of points for integration at each attempt.

Why is "sum" there on the right side of the assignment? Matlab isn't my strong suit, but I believe that sum() is intended to be used on arrays.

In the code snippet below, the variable i is set as an array of integers, so xi, xi1 and xi2 will be arrays, as well as f(xi) and so on.

    i = 0:N-1;
    xi = a+2*i*h;
    xi1 = a+2*(i+0.5)*h;
    xi2 = a+2*(i+1)*h;
    S = (h/3)*sum(f(xi)+4*f(xi1)+f(xi2));

 

[ver_mathstats]

You have

function I=main_simpson(a,b,tol)

So the function will return the value of I, which is not what you calculate. You calculate the integral into S.

Note also that you do not follow what the question asks with regards to the number of points for integration at each attempt.In the code snippet below, the variable i is set as an array of integers, so xi, xi1 and xi2 will be arrays, as well as f(xi) and so on.

    i = 0:N-1;
    xi = a+2*i*h;
    xi1 = a+2*(i+0.5)*h;
    xi2 = a+2*(i+1)*h;
    S = (h/3)*sum(f(xi)+4*f(xi1)+f(xi2));

Yes I realized it was such a silly typo causing issues which is my mistake, I fixed it and now it works