MATLAB: Is the Simpson’s 3/8 code not producing the correct values

numerical integration

Hi,
I am working on some simple numerical quadrature methods, and I am trying to get the Simpson's 3/8 method to work using the following code:
function I = SimpThreeEight(f, a, b, n)
h = (b-a)/n;
S =feval(f,a);
for i = 1 : 3: n-1
x(i) = a + h*i;
S = S + 3*feval(f, x(i));
end
for i = 2 : 3: n-2
x(i) = a + h*i;
S = S + 3*feval(f, x(i));
end
for i = 3 : 3: n-3
x(i) = a + h*i;
S = S + 2*feval(f, x(i));
end
S = S + feval(f, b);
I = 3*h*S/8;
However, using test data with know values my approximations are all off. Can someone identify why?
Thanks!

Best Answer

The upper limits in the first two for-loops are not right. They should be:
for i = 1:3:n-2
  x(i) = a + h*i;
  S = S + 3*feval(f, x(i));
end
for i = 2:3:n-1
  x(i) = a + h*i;
  S = S + 3*feval(f, x(i));
end
Your second for-loop: "for i = 2:3:n-2" incorrectly leaves out the term with 3*feval(f,x(n-1)).
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