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Sbornik: Mathematics, 2010, Volume 201, Issue 1, Pages 79–101
DOI: https://doi.org/10.1070/SM2010v201n01ABEH004066 (Mi sm7538) 		 
This article is cited in 8 scientific papers (total in 10 papers)

The asymptotic behaviour of the solution to a system of differential equations with a small parameter and singular initial point

A. M. Il'ina, Yu. A. Leonychevb, O. Yu. Khachayc

a Chelyabinsk State University
b "IT Ènigma" Ltd.
c Ural State University
English version PDF (336 kB) Citations (10) Russian version article
References:
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DOI: https://doi.org/10.1070/SM2010v201n01ABEH004066
Abstract: The initial value problem for a system of nonlinear ordinary differential equations with a small parameter multiplying the highest derivative is investigated. In a neighbourhood of the initial point the asymptotic behaviour of the solution has quite a complicated structure. A uniform asymptotic approximation to the solution up to an arbitrary power of the small parameter is constructed and substantiated.
Bibliography: 3 titles.
Keywords: asymptotic expansion, small parameter, initial value problem, matching method.
Received: 11.02.2009
Bibliographic databases:
UDC: 517.928
MSC: Primary 34E05, 34E15; Secondary 34A34, 34E13
Language: English
Original paper language: Russian
Citation: A. M. Il'in, Yu. A. Leonychev, O. Yu. Khachay, “The asymptotic behaviour of the solution to a system of differential equations with a small parameter and singular initial point”, Sb. Math., 201:1 (2010), 79–101
Citation in format AMSBIB
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\paper The asymptotic behaviour of the solution to a~system of differential equations with a~small parameter and singular initial point
\jour Sb. Math.
\yr 2010
\vol 201
\issue 1
\pages 79--101
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  • https://doi.org/10.1070/SM2010v201n01ABEH004066
  • https://www.mathnet.ru/eng/sm/v201/i1/p81
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:835
    Russian version PDF:345
    English version PDF:11
    References:76
    First page:81
     
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