cccccc 11.5a
      function ff(x)
      ff=0.5*x*x
      return
      end 

      subroutine split(x,x_p,x_n)
      x_p=0.0
      x_n=0.0
      if(x.gt.0.0) x_p=x   ! x+
      if(x.lt.0.0) x_n=x   ! x-
      return
      end

      function fminmod(a,b)
      if(abs(a).lt.abs(b)) then 
       fminmod=a
      else
       fminmod=b
      endif
      return
      end      

      program main
      parameter(ngrid=100,cfl=0.2,toll=1.d-8)
      dimension x(ngrid+1),n(ngrid+1),u(ngrid+1)
      dimension s(ngrid+1),s_p(ngrid+1),s_n(ngrid+1)
!     s(i) for  s i+1/2
      dimension du(ngrid+1),fflux(ngrid+1)
      ttotal=1.0
      xl=-10.0
      xr=10.0
      dx=(xr-xl)/(ngrid+1)
      do i=1,ngrid+1
       x(i)=xl+dx*(i-1)
       if(x(i).lt.0.0.or.x(i).gt.1.0) then
         u(i)=0.0
       else
         u(i)=2.0
       endif
      enddo
      dt=cfl*dx
      time=dt
      r=dt/dx

10    continue
      do i=1,ngrid
       du(i)=u(i+1)-u(i)
       if(abs(du(i)).lt.toll) then
        s(i)=u(i+1)
       else
        s(i)=(ff(u(i+1))-ff(u(i)))/du(i)
       endif
       call split(s(i),s_p(i),s_n(i))
      enddo
      do 5 i=2,ngrid-1
      du1=du(i)
      if(s(i).gt.0.0) then
       du2=du(i-1)
      else 
       du2=du(i+1)
      endif
      dw=fminmod(du1,du2)
      aa=abs(s(i))
      fflux(i)=0.5*aa*(1-r*aa)*dw     
5     continue
      if(s(1).gt.0.0) then
       dw=du(1)
      else
       dw=fminmod(du(1),du(2))
      endif
      aa=abs(s(1))
      fflux(1)=0.5*aa*(1-r*aa)*dw    
      if(s(ngrid).lt.0.0) then
       dw=du(ngrid)
      else
       dw=fminmod(du(ngrid),du(ngrid-1))
      endif
      aa=abs(s(ngrid))
      fflux(ngrid)=0.5*aa*(1-r*aa)*dw    
      do 15 i=2,ngrid
       u(i)=u(i)-r*(s_p(i-1)*du(i-1)+s_n(i)*du(i))
     $          -r*(fflux(i)-fflux(i-1))
15    continue 
      u(1)=0.0
      u(ngrid+1)=0.0 
      time=time+dt
      if(time.lt.ttotal) goto 10

      write(*,*)'time=',time
      write(*,*)'results are recorded in the file fort.1'
      write(*,*)'in the following form'
      write(*,*)'coordinate - conservative method - nonconservative
     $ method'
      do i=1,ngrid+1
       write(1,*)x(i),u(i)
      enddo
      return
      end