This is the idl code used to produce the solution/graph to the given problem by using the Relation Method.

PRO relax1
   string1=''
   niter = 74
   phi=fltarr(11,11)
   phi(*,10)=1.
   contour,phi
   read,string1
   FOR i=1,niter DO BEGIN
      phi(1:9,1:9)= $
         (phi(0:8,1:9) + phi(2:10,1:9) + $
         phi(1:9,0:8) + phi(1:9,2:10))/4.
      contour,phi,levels=findgen(8)/10.+.1, $
         /follow, $
         title='PHI after'+string(i)+'iteration(s)', $
         xtitle="x axis", ytitle="y axis"        
         ; if i mod (niter/10) eq 0 THEN $
          read,string1
   ENDFOR

  ; print, phi
    contour,phi,levels=findgen(8)/10.+.1, $
         /follow, $
         title='PHI after'+string(i)+'iteration(s)', $
         xtitle="x axis", ytitle="y axis"
   WRITE_GIF,'idl.gif',tvrd()
  ;WRITE_BMP,'idl.bmp',BYTSCL(phi,MAX=32)
  save

END