C*******************************************************************************
C
        subroutine check1(m,n,u,u1,ee)
        implicit double precision (a-h,o-z)
        dimension u(0:m,0:n), u1(0:m,0:n)

        ee = 0.0d0

        do 10 i=0,m
           do 20 j=0,n
              t = abs(u(i,j) - u1(i,j) )
              if(t.ge.ee) ee = t
 20        continue
 10     continue

        return
        end

C*******************************************************************************
  
        subroutine copymat1(m,n,x,y)
        implicit double precision (a-h,o-z)
        dimension x(0:m,0:n),y(0:m,0:n)

        do 10 i=0,m
          do 20 j=0,n
                x(i,j) = y(i,j)
 20     continue
 10     continue

        return
        end

C*******************************************************************************
C
        subroutine check5(m,n,i0,j0,u,u1,ee)
        implicit double precision (a-h,o-z)
        dimension u(0:m,0:n), u1(0:m,0:n)

        ee = 0.0d0

        do 10 i=0,m
        do 20 j=0,n
        t = abs(u(i,j) - u1(i,j) )

        if(t.ge.ee) then
            ee = t
            i0 = i
            j0 = j
        endif

 20     continue
 10     continue

        return
        end

C-------------------------------------------------------------------------------

        subroutine copyvec(n,a,b)

C--------- copyvec copys the vector b into a.

        implicit double precision (a-h,o-z)
        dimension a(n),b(n)

        do 10 i=1,n
           a(i) = b(i)
 10     continue

        return
        end

C*******************************************************************************

        double precision function delcos(x,h)
        implicit double precision (a-h,o-z)
        t = abs(x)
        pi = datan(1.0d0)*4.0d0
        if (t .le. 2.0d0*h) then
           delcos= (1.0d0 + dcos(pi*t/(2.0d0*h)) )/(4.0d0*h)
        else
           delcos = 0.0d0
        endif
           return
        end