Print Email Facebook Twitter On the multiple scales perturbation method for difference equations Title On the multiple scales perturbation method for difference equations Author Van Horssen, W.T. Ter Brake, M.C. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2008-06-04 Abstract In the classical multiple scales perturbation method for ordinary difference equations (O Delta Es) as developed in 1977 by Hoppensteadt and Miranker, difference equations (describing the slow dynamics of the problem) are replaced at a certain moment in the perturbation procedure by ordinary differential equations (ODEs). Taking into account the possibly different behavior of the solutions of an O Delta E and of the solutions of a nearby ODE, one cannot always be sure that the constructed approximations by the Hoppensteadt-Miranker method indeed reflect the behavior of the exact solutions of the O Delta Es. For that reason, a version of the multiple scales perturbation method for O Delta Es will be presented and formulated in this paper completely in terms of difference equations. The goal of this paper is not only to present this method, but also to show how this method can be applied to regularly perturbed O Delta Es and to singularly perturbed, linear O Delta Es. Subject Ordinary difference equationMultiple scales perturbation methodRegularly and singularly perturbed problemsAsymptotic validity To reference this document use: http://resolver.tudelft.nl/uuid:7f26ce2b-3449-42eb-b7f5-3c95e8aec211 DOI https://doi.org/10.1007/s11071-008-9373-z Publisher Springer ISSN 1573-269X Source Nonlinear Dynamics, 55 (4), 2009 Part of collection Institutional Repository Document type journal article Rights (c) 2008 The Authors Files PDF horssen-2009.pdf 514.38 KB Close viewer /islandora/object/uuid:7f26ce2b-3449-42eb-b7f5-3c95e8aec211/datastream/OBJ/view