I with Fortran 90 : Simpson's rule

[bigev234]

Is the program in this case a good one to use for simpson's composite rule because it gives a value with a very small difference when entering an ood number compared to an even number when simpson's composite needs only an even number of intervals

 

[alphysicist]

Is the program in this case a good one to use for simpson's composite rule because it gives a value with a very small difference when entering an ood number compared to an even number when simpson's composite needs only an even number of intervals

I think I would have to disagree with that. The difference is not small at all.

The value of the integral (integrating exp(-x) from 0 to 1) should be 0.63212 to five digits.

When using n=100 intervals, you get that value; if you use n=101 intervals, you get 0.628448. That's about a half a percent difference, which I would say is a huge error for this integral.


For that matter, you can just replace the function given in the program with 1; that is, calculate the integral of 1 from 0 to 1. Of course it should be give 1, right? But the results are:

n=100 ===> integral=1.
n=101 ===> integral=0.990099


The error formula predicts zero error for this type of integral. But for an odd number of intervals it is very close to 1% error--much too large for the integral of a constant. I would say you need to use an even number of subintervals.

 

[fahad20]

hellloo..how can i make my compoosite simpson fortran code general.i mean...take the function as user's input and solve according..heres the codde..what needs to be changed?.

PROGRAM SIMPSON
C NUMERICAL METHODS: FORTRAN Programs, (c) John H. Mathews 1994
C To accompany the text:
C NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992
C Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A.
C This free software is complements of the author.
C
C Algorithm 7.2 (Composite Simpson Rule).
C Section 7.2, Composite Trapezoidal and Simpson's Rule, Page 365
C
INTEGER M
REAL A,B,Srule
CHARACTER*60 ANS*1,DFUN,FUN
EXTERNAL F
10 CALL INPUTS(A,B,M,DFUN,FUN)
CALL SIMPRU(F,A,B,M,Srule)
CALL RESULT(A,B,M,Srule,DFUN,FUN)
WRITE(9,*)'WANT TO TRY ANOTHER INTERVAL ? <Y/N> '
READ (9,'(A)') ANS
IF (ANS.EQ.'Y' .OR. ANS.EQ.'y') GOTO 10
END

REAL FUNCTION F(X)
REAL X
F=X/(1+X*X)
RETURN
END

SUBROUTINE PRINTFUN(DFUN,FUN)
CHARACTER*(*) DFUN,FUN
FUN ='X/(1+X*X)'
DFUN='X/(1+X*X) DX'
RETURN
END

SUBROUTINE SIMPRU(F,A,B,M,Srule)
INTEGER K,M
REAL A,B,H,Sum,SumEven,SumOdd,Srule,X
EXTERNAL F
H=(B-A)/(2*M)
SumEven=0
DO K=1,(M-1)
X=A+H*2*K
SumEven=SumEven+F(X)
ENDDO
SumOdd=0
DO K=1,M
X=A+H*(2*K-1)
SumOdd=SumOdd+F(X)
ENDDO
Sum=H*(F(A)+F(B)+2*SumEven+4*SumOdd)/3
Srule=Sum
RETURN
END

SUBROUTINE XSIMPRU(F,A,B,M,Srule)
C This subroutine uses labeled DO loop(s).
INTEGER K,M
REAL A,B,H,Sum,SumEven,SumOdd,Srule,X
EXTERNAL F
H=(B-A)/(2*M)
SumEven=0
DO 10 K=1,(M-1)
X=A+H*2*K
SumEven=SumEven+F(X)
10 CONTINUE
SumOdd=0
DO 20 K=1,M
X=A+H*(2*K-1)
SumOdd=SumOdd+F(X)
20 CONTINUE
Sum=H*(F(A)+F(B)+2*SumEven+4*SumOdd)/3
Srule=Sum
RETURN
END

SUBROUTINE INPUTS(A,B,M,DFUN,FUN)
INTEGER I,M
REAL A,B
CHARACTER*(*) DFUN,FUN
CALL PRINTFUN(DFUN,FUN)
DO 10 I=1,18
WRITE(9,*)' '
10 CONTINUE
WRITE(9,*)' SIMPSON`S RULE IS USED TO COMPUTE AN APPROXIMATION'
WRITE(9,*)' '
WRITE(9,*)'FOR THE VALUE OF THE DEFINITE INTEGRAL:'
WRITE(9,*)' '
WRITE(9,*)' '
WRITE(9,*)' B'
WRITE(9,*)' /'
WRITE(9,*)' | ',DFUN
WRITE(9,*)' /'
WRITE(9,*)' A'
WRITE(9,*)' '
WRITE(9,*)' '
WRITE(9,*)'ENTER THE LEFT ENDPOINT A = '
READ(9,*) A
WRITE(9,*)' '
WRITE(9,*)'ENTER THE RIGHT ENDPOINT B = '
READ(9,*) B
WRITE(9,*)' '
WRITE(9,*)'THE NUMBER OF SUBINTERVALS USED IS 2*M'
WRITE(9,*)' ENTER THE NUMBER M = '
READ(9,*) M
WRITE(9,*)' '
RETURN
END

SUBROUTINE RESULT(A,B,M,Srule,DFUN,FUN)
INTEGER I,M
REAL A,B,Srule
CHARACTER*(*) DFUN,FUN
CALL PRINTFUN(DFUN,FUN)
DO 10 I=1,18
WRITE(9,*)' '
10 CONTINUE
WRITE(9,*)' ',B
WRITE(9,*)' /'
WRITE(9,*)' |'
WRITE(9,*)Srule,' ~ | ',DFUN
WRITE(9,*)' |'
WRITE(9,*)' /'
WRITE(9,*)' ',A
WRITE(9,*)' '
WRITE(9,*)' '
WRITE(9,*)'AN APPROXIMATE VALUE FOR THE DEFINITE INTEGRAL OF'
WRITE(9,*)' '
WRITE(9,*)' '
WRITE(9,*)'F(X) = ',FUN
WRITE(9,*)' '
WRITE(9,*)' '
WRITE(9,*)'TAKEN OVER [',A,' ,',B,' ] WAS FOUND.'
WRITE(9,*)' '
WRITE(9,*)'SINCE M = ',M,', THERE WERE ',2*M,' SUBINTERVALS.'
WRITE(9,*)' '
WRITE(9,*)'THE SIMPSON RULE APPROXIMATION IS ',Srule
WRITE(9,*)' '
RETURN
END