A class of multi-scales nonlinear difference equations

Abstract

In this paper, we give an iteration algorithm to compute asymptotic solutions for a class of nonlinear difference equations containing small parameters of multiple scales. We consider two kinds of perturbations. Mathematics Subject Classification: 39A10

Boundary Value Problem for a Two-Time-Scale Nonlinear Discrete System

“…by using an algorithmic technique we developed firstly for perturbed difference equations (see [10], [11], [16], [17], [18], [19]). Recently, many researchers have studied discrete versions of boundary value problems (BVPs) (see [1], [4], [5], [8]), and applications of two-point BVP algorithms arise in pollution control problems, nuclear reactor heat transfer and vibration.…”

Nonlinear perturbed difference equations

“…In [10,13], we have elucidated that we could define homogeneous asymptotic expansions for singularly perturbed difference equations bypassing the correction terms and we gave applications to control problems in [14][15][16][17]. Recently in [18,19], we used this homogeneous method for a class of nonlinear equations giving explicitly asymptotic solutions up to any order. The plan of this paper is to extend this procedure based on Faa Di Bruno formula [6] and contraction mapping principle, to a wide class of nonlinear singularly-perturbed difference equations.…”