Advances in Difference Equations
Volume 2006 (2006), Article ID 19214, 12 pages
Perturbation method for linear difference equations with small
Laboratoire de Mathématiques, Département de Mathématiques, Université de Haute Alsace, 4 rue des Frères Lumière, Mulhouse 68093, France
Received 14 December 2005; Revised 5 April 2006; Accepted 26 April 2006
Copyright © 2006 Tahia Zerizer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider a boundary value problem for a linear difference equation with
several widely different coefficients. We study the existence and uniqueness
of its solution and we give successive asymptotic approximations for this
solution, obtained by a simple iterative method. This method improves the
singular perturbation method, it offers considerable reduction and
simplicity in computation since it does not require to compute boundary
layer correction solutions.