This article is cited in 1 paper

Mathematics

A method to study the Cauchy problem for an arbitrary order singularly perturbed linear homogeneous differential equation

E. E. Bukzhalev

Faculty of Physics, Lomonosov Moscow State University

Abstract: We construct a sequence converging to the solution to the Cauchy problem for a singularly perturbed, linear, homogeneous differential equation of any order. This sequence is asymptotic in the following sense: the distance (with respect to the norm of the space of continuous functions) between its $n$th element and the solution to the problem is proportional to the $(n+1)$th power of the perturbation parameter.

Key words: singular perturbations, Banach fixed-point theorem, asymptotic iteration method, boundary function method.

UDC: 517.928.2

Received: 01.02.2017

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2018, 73:2, 41–49

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