simpson.f90

!-----------------------------------------------------------------------
! SUBROUTINE: SIMPSON.F90
!-----------------------------------------------------------------------
!
! This subroutine performs the numerical integration of a function f(x) 
! in the  interval [a,b] by using the Simpson rule. 
! The arguments of the subroutine are the following:
!
!     > a: Lower limit of the integration region
!     > b: Upper limit of the integration region
!     > N: Number of points in the integration grid
!     > f: Function to be integrated, it is an N-element array containing 
!          the value of the function in the grid points
!
!------------------------------------------------------------------------
!
! Adrián Macía (2013)
!
!------------------------------------------------------------------------

real (kind=8) function simpson(a,b,N,f)

implicit none

real (kind=8)    :: a,b,dx
real (kind=8)    :: s1,s2
integer (kind=4) :: j,N

real (kind=8), dimension(0:N) :: f

dx = (b-a)/real(N)

s1 = 0.d0
s2 = 0.d0

do j=0,N/2-1
   s1 = s1+f(2*j+1)
   s2 = s2+f(2*j+2)
end do

!do j=1,N/2
!   simpson = simpson+4.d0*f(2*j-1)
!end do

!do j=1,N/2-1
!   simpson = simpson+2.d0*f(2*j)
!end do

simpson = dx*(f(0)+2.d0*s2+4.d0*s1-f(N))/3.d0

return
end function simpson

!-----------------------------------------------------------------------