Compact Simpson's 3/8 Rule(??)

[Csaba Tizedes]

(12-13-2015 05:05 PM)Namir Wrote:  

Code:

h = (b - a) / n
sum = f(a) + f(b)

For i = 1 To n - 1
  c = 2 + Sgn(i Mod 3)
  sum = sum + c * f(a + i * h)
Next

result = 3 / 8 * h * sum

I like your FOR loop and the use of the SIGN function!!

Now we have a compact implementation that performs one function summation per iteration and with minimum calculations. Your pseudo-code version looks simple and very nice.

Or maybe:

Code:

h = (b - a) / n
sum = f(a) + f(b)

For i = 1 To n - 3 Step 3
  sum = sum + 3 * f(a + i * h) + 3 * f(a + (i+1) * h) + 2 * f(a + (i+2) * h)
Next

result = 3 / 8 * h * sum

Csaba