, Volume 69, Issue 4, pp 1509-1516,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 29 Feb 2012

Solving systems of nonlinear difference equations by the multiple scales perturbation method

Abstract

In this paper, we apply an improved version of the multiple scales perturbation method to a system of weakly nonlinear, regularly perturbed ordinary difference equations. Such systems arise as a result of the discretization of a system of nonlinear differential equations, or as a result in the stability analysis of nonlinear oscillations. In our procedure, asymptotic approximations of the solutions of the difference equations will be constructed which are valid on long iteration scales.