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=$\frac{h}{3}$ {f_start+f_end+2Ʃf_even+4Ʃf_odd}

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=[itex]\frac{(X_max-X_min)}{N}[/itex]

oddweight=4

evenweight=2

DO i=1,256

I=$\frac{h}{3}$ {f_start+f_end+2Ʃf_even+4Ʃf_odd}


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

 

[Nandos]

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

 

[SteamKing]

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?

 

[Chestermiller]

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=ײ using Simpson's Rule on FORTRAN

 

[Chestermiller]

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=ײ 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

 

[Chestermiller]

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

 

[Chestermiller]

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]

Nope i don't know and can you please help me.

 

[Chestermiller]

Nope i don't know and can you please help me.

You need to get yourself a textbook on FORTRAN and do a little studying. The information you need to do this assignment is a little to extensive for a format like PF.