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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 1, Pages 33–45 (Mi zvmmf193)  
This article is cited in 1 scientific paper (total in 1 paper)

Asymptotics of a second-order differential equation with a small parameter in the case when the reduced equation has two solutions

S. F. Dolbeeva, E. A. Chizh

Chelyabinsk State University, ul. Brat'ev Kashirinykh 129, Chelyabinsk, 454021, Russia
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Abstract: The boundary value problem for a second-order nonlinear ordinary differential equation with a small parameter multiplying the highest derivative is examined. It is assumed that the reduced equation has two solutions with intersecting graphs. Near the intersection point, the asymptotic behavior of the solution to the original problem is fairly complex. A uniform asymptotic approximation to the solution that is accurate up to any prescribed power of the small parameter is constructed and justified.
Key words: asymptotic expansion of a solution, differential equation with a small parameter, boundary value problem, matching of asymptotic expansions.
Received: 02.07.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 1, Pages 30–42
DOI: https://doi.org/10.1007/s11470-008-1003-9
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: S. F. Dolbeeva, E. A. Chizh, “Asymptotics of a second-order differential equation with a small parameter in the case when the reduced equation has two solutions”, Zh. Vychisl. Mat. Mat. Fiz., 48:1 (2008), 33–45; Comput. Math. Math. Phys., 48:1 (2008), 30–42
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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