ANÁLISE DE UM PROBLEMA DE PERTURBAÇÃO SINGULAR VIA MÉTODO DAS EXPANSÕES EMPARELHADAS

Abstract

Finding the exact solution to a mathematical model can become a difficult or even impossible task. Thus, it is essential that techniques for approximating solutions be studied and employed whenever it is not possible to obtain exact solutions. In this article the perturbation theory will be considered to obtain the solution of a differential equation with singular perturbation, where it will be shown that the standard approach does not provide satisfactory results. Therefore, a new approach is needed, in this case, the so-called method of matched asymptotic expansions will be used.

Keywords: Singular perturbation; Formal asymptotic solution; Asymptotic expansion; Asymptotic matching