Simpson's Rule Implementation trick?

[Namir]

By initializing the sum as:

Code:

sum = f(a) + f(b) + 4*f(a+h)

Instead of the usual expression:

Code:


sum = f(a) + f(b)

We can then iterate over the terms multiplied by 2 and then by 4. We can do this:

Code:

for i=2 to n step 2
  sum = sum + 2*f(a+i*h) + 4*f(a + (i+1)*h)
next

Or, borrowing from the old threads:

Code:

c = 2
for i=2 to n
  x = x + h
  sum = sum + c*f(x)
  c = 6 - c
next