Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2018, Number 2, Pages 3–12 (Mi vmumm15)  
This article is cited in 1 scientific paper (total 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
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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.
Received: 01.02.2017
English version:
Moscow University Mathematics Bulletin, 2018, Volume 73, Issue 2, Pages 41–49
DOI: https://doi.org/10.3103/S0027132218020018
Bibliographic databases:
Document Type: Article
UDC: 517.928.2
Language: Russian
Citation: E. E. Bukzhalev, “A method to study the Cauchy problem for an arbitrary order singularly perturbed linear homogeneous differential equation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, no. 2, 3–12; Moscow University Mathematics Bulletin, 73:2 (2018), 41–49
Citation in format AMSBIB
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