MODULE PARAM
    IMPLICIT NONE
    INTEGER, PARAMETER  :: SP = KIND(1.0)
    INTEGER, PARAMETER  :: DP = KIND(1.D0)

MODULE BURGER_2
   USE PARAM
   IMPLICIT NONE

   REAL(DP), PARAMETER   :: x0=0. , xF= 5.
   REAL(DP), PARAMETER   :: t0=0. , tF= 1.0
   REAL(DP), PARAMETER   :: dx=0.01, dt=0.1
   INTEGER , PARAMETER   :: N= CEILING((xF-x0)/dx)
   INTEGER , PARAMETER   :: M= CEILING((tF-t0)/dt)
   REAL(DP), PARAMETER   :: nu = 2D-4
   REAL(DP), PARAMETER   :: pi=3.14159265358979323846

SUBROUTINE BURGER_EXPLICIT (x,t,u)
       USE PARAM
       REAL(DP), DIMENSION(N+1)     :: x
       REAL(DP), DIMENSION(M+1)     :: t
       REAL(DP), DIMENSION(N+1,M+1) :: U
       REAL(DP)   :: r,k
       INTEGER    :: i,j,stat



       x(1:N+1)       = (/ ( x0+dx*(i-1) , i=1,N+1 ) /)
       t(1:M+1)       = (/ (t0+ dt*(j-1) , j=1,M+1 ) /)
       U(1:N+1,1:M+1) = RESHAPE((/(((sin(2*pi*(i-1)/N)), i=1,N+1), j=1,M+1)/),(/N+1,M+1/))

       U(1,:)   = x0
       U(N+1,:) = xF

       U(:,1)   = t0
       U(:,M+1) = tF



       r = nu*DT/DX**2
       k = DT/(2*DX)

       DO J=2,M
        DO I=2,N
          U(i,j+1) = r*u(i+1,j)+(1-2*r)*u(i,j)+r*u(i-1,j) - k*u(i,j)*(u(i+1,j)-u(i-1,j))
        END DO
       END DO

       !DO j=1,M+1
       OPEN(10,file='bur1.dat',STATUS='UNKNOWN',IOSTAT=stat)
        IF (STAT .NE. 0) THEN
         WRITE(6,FMT='(A)')'Error opening File ''bur1.dat'' (EXIT1)'
         STOP
        ELSE
          WRITE(10,FMT='(2F20.5)') (x(i), u(i,10), i=1,N)        !((u(i,j) , i=1,N+1), J=1,M+1)
          !WRITE(10,*)
          !WRITE(10,FMT='(2F20.5)') (x(i), u(i,2), i=1,N)        !((u(i,j) , i=1,N+1), J=1,M+1)
          WRITE(6,'(50("-"))')
       !END DO
        END IF

       RETURN
     END SUBROUTINE

  END MODULE