!!!!!!!!!!!!!!!!!!!!!!!!!!! Program 2.5 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! !
! Please Note: !
! !
! (1) This computer program is written by Tao Pang in conjunction with !
! his book, "An Introduction to Computational Physics," published !
! by Cambridge University Press in 1997. !
! !
! (2) No warranties, express or implied, are made for this program. !
! !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
PROGRAM INTEGRAL
!
! Main program for evaluation of an integral with integrand
! sin(x) in the region of [0,pi/2]. Copyright (c) Tao Pang 1997.
!
IMPLICIT NONE
INTEGER, PARAMETER :: N=9
INTEGER :: I
REAL :: PI,H,S
REAL, DIMENSION (N) :: X,F
!
PI = 4.0*ATAN(1.0)
H = PI/(2*(N-1))
DO I = 1, N
X(I) = H*(I-1)
F(I) = SIN(X(I))
END DO
CALL SIMP (N,H,F,S)
WRITE (6, "(F16.8)") S
END PROGRAM INTEGRAL
!
SUBROUTINE SIMP (N,H,FI,S)
!
! Subroutine for integration over f(x) with the Simpson rule. FI:
! integrand f(x); H: interval; S: integral. Copyright (c) Tao Pang 1997.
!
IMPLICIT NONE
INTEGER, INTENT (IN) :: N
INTEGER :: I
REAL, INTENT (IN) :: H
REAL :: S0,S1,S2
REAL, INTENT (OUT) :: S
REAL, INTENT (IN), DIMENSION (N) :: FI
!
S = 0.0
S0 = 0.0
S1 = 0.0
S2 = 0.0
DO I = 2, N-1, 2
S1 = S1+FI(I-1)
S0 = S0+FI(I)
S2 = S2+FI(I+1)
END DO
S = H*(S1+4.0*S0+S2)/3.0
!
! If N is even, add the last slice separately
!
IF (MOD(N,2).EQ.0) S = S &
+H*(5.0*FI(N)+8.0*FI(N-1)-FI(N-2))/12.0
END SUBROUTINE SIMP