c===========================================================
c     chk_tlsoda:  Program to check the output of tlsoda 
c     by applying a second-order discretization of the ODE
c     to the computed solution.  
c
c     Output is dt and the RMS value of the residual of the 
c     O(dt^2) discretization, which should itself be 
c     approximately O(dt^2); refer to class notes for more
c     details.
c===========================================================
      program       chk_tlsoda

      implicit      none

      integer       maxnt
      parameter   ( maxnt = 100 000 )

      real*8        t(maxnt),     u(maxnt)
      real*8        hm2,          rmsres
      integer       nt,           it
 
      call dvvfrom('-',t,u,nt,maxnt)
c-----------------------------------------------------------
c     Will assume that 't' defines a *uniform* mesh.
c-----------------------------------------------------------
      hm2 = 1.0d0 / (t(2) - t(1))**2
      rmsres = 0.0d0
      do it = 2 , nt - 1
         rmsres = rmsres + 
     &      ( hm2 * (u(it+1) - 2.0d0 * u(it) + u(it-1)) +
     &        u(it) )** 2
      end do
      rmsres = sqrt(rmsres / (nt - 2))
      write(*,*) t(2) - t(1), rmsres
      
      stop

900   continue
         write(0,*) 'usage: chk_tsloda'
         write(0,*) ' '
         write(0,*) '       Reads (x_i, u_i) pairs from '//
     &                      'standard input'
      stop
 
      end