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.
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
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\by A.~M.~Il'in, Yu.~A.~Leonychev, O.~Yu.~Khachay
\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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Linking options:
https://www.mathnet.ru/eng/sm7538
https://doi.org/10.1070/SM2010v201n01ABEH004066
https://www.mathnet.ru/eng/sm/v201/i1/p81
This publication is cited in the following 10 articles:
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