@Doug Meade 

Thanks for your remark. G(x,y) is a trigonometric function.

To Carl

It's Ok carl. I would like thank you for your help.

To tomleslie

Thank you for your replies.

Yes a long program in a Maple worksheet.I can't post the worksheet but I give the last line:G :=subs(x=x1,  y=y1, expr1); i obtain as result [La longueur de sortie dépasse la limite de 1% noeuds]. x1, y1, expr1 are too long expressions.

@Axel Vogt I only simplified the code by taking dt*mu(k)/dz=dt/ep(k)/dz=1 

@Carl Love Thank you, I'll try this

@tomleslie Thank you for your advice advices.

This Matlab code is given in the paper  '1D-FDTD using MATLAB' by Hung Loui, Student Member, IEEE. I want to find a way to implement the FDTD equations in Maple software.

@Carl Love

 Thank you for your help. I tried with

restart;

M := 20; T := 25; Ex := Array(1 .. M+1); Hy := Array(1 .. M);#I want to find Ex[k] and Hy[k] for k=1...M and                  # for  the time t=1..T,but this  program gave me just Ex[1] for the time t=1..T.  for more               # informations see the paper '1D-FDTD using MATLAB' by Hung Loui, Student Member, IEEE

for t to T do

Ex[1] := exp(-t);     #I mean Ex[1]

for k to M do

Hy[k] := Hy[k]-Ex[k+1]+Ex[k]; 

od;

for k from 2 to M do

Ex[k] := Ex[k]-Hy[k]+Hy[k-1];

od;

od;