problem with coding pseudocode

I am trying to code the following pseudo-code to approximate the solution to the 1D linear convection as in the figure:

http://imageshack.us/photo/my-images/708/fig1s.jpg/

Here is what I have done so far,

PROGRAM one_d_linear_convection
IMPLICIT NONE
INTEGER::i,it,nx,nt,k
DOUBLE PRECISION::dx,dt,c
DOUBLE PRECISION,DIMENSION(1:20)::u,un
nx=20
nt=50
dt=0.01
c=1.0
dx=2./(nx-1.)

!initial condition
DO i = 1,nx
	IF (i*dx>=0.5 .and. i*dx<=1) THEN
		u(i) = 2	
    ELSE
  		u(i) = 1
	ENDIF
!     WRITE(*,*)i,u(i)
ENDDO

!Finite Difference

DO it=1,nt
DO k=0,nx-1
   un(k)=u(k)
DO i=2,nx-1

u(i) = un(i) - c*dt/dx*(un(i)-un(i-1))


WRITE(*,*)i,u(i)


ENDDO
ENDDO
ENDDO  



END

My problem is I cant figure a way out to see the arrays and the u value at x=1 and 20. Any help would be highly appreciated.

Thanks!

Do these changes get closer to what you want PROGRAM one_d_linear_convection IMPLICIT NONE INTEGERi,it,nx,nt,k DOUBLE PRECISIONdx,dt,c, x DOUBLE PRECISION,DIMENSION(1:20)::u,un ! nx=20 nt=50 dt=0.01 c=1.0 dx=2./(nx-1.)

!initial condition 
DO i = 1,nx 
   x = i*dx
   IF (x>=0.5 .and. x<=1.0) THEN 
     u(i) = 2    
   ELSE 
     u(i) = 1 
   ENDIF 
!     WRITE(*,*)i,u(i) 
END DO 

!Finite Difference 

DO it=1,nt 
!
  DO k=1,nx         !   0,nx-1 
    un(k)=u(k) 
  ENDDO 
!
  DO i=2,nx-1 
    u(i) = un(i) - c*dt/dx*(un(i)-un(i-1)) 
  ENDDO 
!
  DO i=1,nx 
    WRITE(*,*) it,i,u(i) 
  ENDDO 
!
ENDDO  

END 

You can import the output from the program into excel and chart the results.

You now have flow in only one direction ? why not have : u(i) = un(i) - cdt/dx(un(i)-un(i-1)) & - cdt/dx(un(i)-un(i+1))

A better solution for more itterations, printing fewer results and allowing flow both ways could be PROGRAM one_d_linear_convection IMPLICIT NONE INTEGER :: i,it,nx,nt,k REAL8 :: dx,dt,c, x REAL8,DIMENSION(40) :: u,un ! nx = size (u) dt = 0.001 ! use a smaller time step nt = 501 c = 1.0 dx = 2./(nx-1.) ! ! initial condition DO i = 1,nx x = idx IF (x>=0.5 .and. x<=1.0) THEN u(i) = 2
ELSE u(i) = 1 ENDIF ! WRITE(,)i,u(i) END DO ! ! Finite Difference DO it=1,nt ! DO k=1,nx ! 0,nx-1 un(k)=u(k) ENDDO ! DO i=2,nx-1 u(i) = un(i) - cdt/dx/2.0 * ( (un(i)-un(i-1)) + (un(i)-un(i+1)) ) ENDDO ! if (mod(it,100)== 1) then ! only print every 0.1 seconds DO i=1,nx WRITE(,) it,i,u(i) ENDDO end if ! ENDDO
! END

That was so nice of you, John. Thank you so much for the codes!

PROGRAM odlc
  IMPLICIT NONE
  INTEGER::i,it
  INTEGER,PARAMETER::nx=20,nt=50
  DOUBLE PRECISION,PARAMETER::dx=2./(nx-1.),dt=0.01,c=1.0
  DOUBLE PRECISION,DIMENSION(nt,nx)::u
  CHARACTER(len=32)::fmt
  WRITE(fmt,*)'(F5.2,',nt,'F5.2)'

!initial_condition                                             
  DO i = 1,nx
     IF(i*dx>=0.5 .and. i*dx<=1) THEN
        u(1,i)=2
     ELSE
        u(1,i)=1
     ENDIF
  ENDDO

!Finite_Difference
  DO it=2,nt
     DO i=2,nx-1
        u(it,i)=u(it-1,i)-c*dt/dx*(u(it-1,i)-u(it-1,i-1))
     ENDDO
  ENDDO

!Write_File
  OPEN(UNIT=200,FILE='tab2.txt',STATUS='REPLACE',ACTION='WRITE')
  DO i=1,nx
    WRITE(200,fmt)dble(i)*dx,u(:,i)
  ENDDO
  CLOSE(UNIT=200)
END PROGRAM odlc