Program Example1
c#######################################################################
c#
c# This is an MPI example on parallel integration
c# Demonstrate here is the serial program.
c#
c# Dr. Kadin Tseng
c# Scientific Computing and Visualization
c# Boston University
c# 1998
c#
c#######################################################################
      implicit none
      integer n, p, i, j
      real h, integral_sum, a, b, integral, pi, ai

      pi = acos(-1.0)   !  = 3.14159...
      a = 0.0           ! lower limit of integration
      b = pi/2.         ! upper limit of integration
      p = 1             ! number of processes (partitions)
      n = 50000           ! number of increment within each process
      h = (b-a)/n/p     ! length of increment

      integral_sum = 0.0      ! stores answer to the integral
      do i=0,p-1        ! sum of integrals over all processes
        ai = a + i*n*h  ! lower limit of integration for partition i
        integral_sum = integral_sum + integral(ai,h,n)
      enddo

      print *,'The integral_sum =', integral_sum
      
      end
      real function integral(ai, h, n)
      implicit none
      integer n, j
      real h, ai, aij

      integral = 0.0                ! initialize integral
      do j=0,n-1                    ! sum integrals
        aij = ai +(j+0.5)*h         ! abscissa mid-point
        integral = integral + cos(aij)*h
      enddo

      return
      end