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Perturbation method for linear difference equations with small parameters

Advances in Difference Equations volume 2006, Article number: 019214 (2006) Cite this article

Abstract

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.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Département de Mathématiques, Université de Haute Alsace, 4 rue des Frères Lumière, Mulhouse, 68093, France

    Tahia Zerizer

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  1. Tahia Zerizer
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Correspondence to Tahia Zerizer.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zerizer, T. Perturbation method for linear difference equations with small parameters. Adv Differ Equ 2006, 019214 (2006). https://doi.org/10.1155/ADE/2006/19214

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  • DOI: https://doi.org/10.1155/ADE/2006/19214

Keywords

  • Differential Equation
  • Boundary Layer
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis