c
c     Numerical Analysis:
c     The Mathematics of Scientific Computing
c     D.R. Kincaid & E.W. Cheney
c     Brooks/Cole Publ., 1990
c
c     Section 9.3
c
c     Example of Finite Difference Method
c
c
c     file: exs93.f
c
      parameter (n=18)
      dimension v(0:n,0:n),x(0:n),y(0:n),u(0:n,0:n)
c
      print *
      print *,' Finite Difference Method'
      print *,' Section 9.3, Kincaid-Cheney' 
      print *
      print *,'    error'
c
      m = 200
      nn = n+1
      h = 1.0/nn 
      do 2 i=0,n+1
         x(i) = i*h
         y(i) = x(i)
 2    continue
      do 3 i=0,n+1
         v(i,0)=g(x(i),0.)
         v(i,n+1)=g(x(i),1.)
	 v(0,i)=g(0.,y(i))
	 v(n+1,i)=g(1.,y(i))
 3    continue
      do 4 k=1,m
         do 4 j=1,n
	    do 4 i=1,n
	       v(i,j) = (v(i-1,j) + v(i+1,j) + v(i,j-1) + v(i,j+1))/4.0
 4    continue
      xmax = 0.0
      do 5 j=0,n
         do 5 i=0,n
            u(i,j) = g(x(i),y(j))
            err = abs(v(i,j) - u(i,j))
            if(err .gt. xmax) xmax = err
 5    continue       
      print 6,xmax
c
 6    format (5x,e13.6)
      stop
      end
c
      real function g(x,y)
      data pi/3.14159 26535 89793/
      g = (10.0e-4)*sinh(3.0*pi*x)*sin(3.0*pi*y)
      return
      end