For a numerical methods class, I need to write a program to evaluate a definite integral with Simpson\'s composite rule. I already got this far (see below), but my answer is
You probably forget to initialize x
before the second loop, also, starting conditions and number of iterations are off. Here is the correct way:
def simpson(f, a, b, n):
h=(b-a)/n
k=0.0
x=a + h
for i in range(1,n/2 + 1):
k += 4*f(x)
x += 2*h
x = a + 2*h
for i in range(1,n/2):
k += 2*f(x)
x += 2*h
return (h/3)*(f(a)+f(b)+k)
Your mistakes are connected with the notion of a loop invariant. Not to get into details too much, it's generally easier to understand and debug cycles which advance at the end of a cycle, not at the beginning, here I moved the x += 2 * h
line to the end, which made it easy to verify where the summation starts. In your implementation it would be necessary to assign a weird x = a - h
for the first loop only to add 2 * h
to it as the first line in the loop.