# Simpson's Rule and Numerical Integration

Nandos
For this problem use Simpson's Rule with N=256 for numerical integration function is y=×^2
and the lower limit is 1 & 3 is the upper limit.

I=$\frac{h}{3}$ {fstart+fend+2Ʃfeven+4Ʃfodd}

Find the numerical integration, using FORTRAN

my solution follows like this:

Program SimpsonRule

IMPLICIT NONE

REAL :: Xmax, Xmin,h , y

INTEGER :: N

Xmax=1.0

Xmin=3.0

N256

contains

h=$\frac{(Xmax-Xmin)}{N}$

oddweight=4

evenweight=2

DO i=1,256

I=$\frac{h}{3}$ {fstart+fend+2Ʃfeven+4Ʃfodd}

integrate y=x^2

print*,I

END DO

END Program SimpsonRule

comment

I have be told that the code must have subroutine, Do statement, function and call if statement.

my problem most start when i have to tell the computer to sum odd number and multiply by factor of 4 and sum the even number also multiply by factor of two.

the answer for the problem is 8.66667

Last edited:

Nandos
the equation BELOW CONTAINS suppose to be : h=(Xmax-Xmin)/N

Staff Emeritus
Homework Helper
Use CODE tags when entering source code to your post. This helps to preserve any spacing.

In the Loop, you can't just throw your I eqn. from the first part of the post directly into the middle of a loop and expect Fortran to make sense of it. More programming is required to obtain the proper calculation of the integral. How is the program to know what 'fodd' and 'feven' are?

Mentor
Hi Nandos. Welcome to Physics Forums.

I don't know what this code is that you have written, but it definitely is not FORTRAN. Have you been assigned any simpler problems to work on before you advanced to a program like this?

Chet

Nandos
This is the simpler problem that we need to work on before we do the hard problem, to make problem simple we suppose to find the integration of Y=×2 using Simpson's Rule on FORTRAN

Mentor
This is the simpler problem that we need to work on before we do the hard problem, to make problem simple we suppose to find the integration of Y=×2 using Simpson's Rule on FORTRAN

Are you saying that this is the first FORTRAN program you will have ever written?

Chet

Nandos
Nope it no but it the first one for integration and Simpsons rule

Mentor
Nope it no but it the first one for integration and Simpsons rule
So you are familiar with Dimension statements, and have used them before?

Nandos
Yes we have

Mentor
Yes we have
Then at least the function F should be dimensioned in your FORTRAN program. Do you know how to set up a do loop to carry out a sum on a subscripted variable?

Nandos