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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 4, Pages 654–661
DOI: https://doi.org/10.7868/S0044466917040056 (Mi zvmmf10561) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On the holomorphic regularization of singularly perturbed systems of differential equations

V. I. Kachalov

National Research University “MPEI”, Moscow, Russia
Full-text PDF (109 kB) Citations (10)
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DOI: https://doi.org/10.7868/S0044466917040056
Abstract: A method for constructing pseudo-holomorphic solutions to strongly nonlinear singularly perturbed systems of differential equations, which a logical continuation of the Lomov regularization method, is proposed. The existence of integrals of such systems, holomorphic in the small parameter, is proven, and sufficient conditions for the convergence of expansion of solutions to these systems in powers of the small parameter in the usual sense are obtained.
Key words: method of regularization, holomorphic regularization, pseudo-holomorphic solution, integrals holomorphic in a small parameter, singularly perturbed systems of differential equations, sufficient conditions for convergence.
Received: 03.02.2016
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 4, Pages 653–660
DOI: https://doi.org/10.1134/S0965542517040054
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: V. I. Kachalov, “On the holomorphic regularization of singularly perturbed systems of differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 57:4 (2017), 654–661; Comput. Math. Math. Phys., 57:4 (2017), 653–660
Citation in format AMSBIB
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    • This publication is cited in the following 10 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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