Original Paper

Nonlinear Dynamics

, Volume 69, Issue 4, pp 1509-1516

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • M. RafeiAffiliated withDelft Institute of Applied Mathematics (DIAM), Delft University of Technology Email author 
  • , W. T. Van HorssenAffiliated withDelft Institute of Applied Mathematics (DIAM), Delft University of Technology

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.

Keywords

Nonlinear difference equation Multiple scales perturbation method Difference operator