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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 12, Pages 2206–2218 (Mi zvmmf9810)  
This article is cited in 6 scientific papers (total in 6 papers)

Power-elliptic expansions of solutions to an ordinary differential equation

A. D. Bruno

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow
Full-text PDF (286 kB) Citations (6)
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Abstract: A rather general ordinary differential equation is considered that can be represented as a polynomial in variables and derivatives. For this equation, the concept of power-elliptic expansions of its solutions is introduced and a method for computing them is described. It is shown that such expansions of solutions exist for the first and second Painlevé equations.
Key words: ordinary differential equation, asymptotic expansion of solutions, elliptic asymptotic behavior, first and second Painlevé equations.
Received: 26.12.2011
Revised: 02.10.2012
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 12, Pages 1650–1661
DOI: https://doi.org/10.1134/S0965542512120056
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: A. D. Bruno, “Power-elliptic expansions of solutions to an ordinary differential equation”, Zh. Vychisl. Mat. Mat. Fiz., 52:12 (2012), 2206–2218; Comput. Math. Math. Phys., 52:12 (2012), 1650–1661
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Full-text PDF :80
    References:38
    First page:18
     
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