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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 5, Pages 807–821
DOI: https://doi.org/10.7868/S0044466915050178 (Mi zvmmf10203) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Flat expansions and their applications

V. P. Varin

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia
Full-text PDF (265 kB) Citations (4)
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DOI: https://doi.org/10.7868/S0044466915050178
Abstract: Polynomial ordinary differential equations (ODEs) near a singular point are considered. Families of solutions to ODEs that are exponentially close to a solution represented by a formal power series are studied. It is shown that, for systems of ODEs in the plane, all solutions of such a family are uniquely determined by a series of flat functions. Flat expansions are poorly understood. The power series involved in flat expansions can converge or diverge. Examples of computations of flat expansions are given, and their applications are considered. A flat expansion of the solution to the Blasius problem at infinity is calculated. It is shown that this asymptotic expansion can be matched with the Blasius power series expansion at the origin.
Key words: asymptotic expansions, flat functions, singularities of ODEs, Blasius problem, boundary layer theory.
Received: 13.10.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 5, Pages 797–810
DOI: https://doi.org/10.1134/S0965542515050164
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
MSC: Primary 34A25; Secondary 41A58
Language: Russian
Citation: V. P. Varin, “Flat expansions and their applications”, Zh. Vychisl. Mat. Mat. Fiz., 55:5 (2015), 807–821; Comput. Math. Math. Phys., 55:5 (2015), 797–810
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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