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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 11, Pages 1806–1814
DOI: https://doi.org/10.31857/S0044466923110170 (Mi zvmmf11643) 		 
General numerical methods

Analyticity and pseudo-analyticity in the small parameter method

V. I. Kachalov, D. A. Maslov

National Research University "Moscow Power Engineering Institute", 111250, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466923110170
Abstract: The small parameter method allows one to construct solutions of differential equations in the form of power series and has become widespread in mathematical physics. In most cases, these series are asymptotically convergent. The aim of this work is to find conditions for the ordinary convergence of series in powers of a small parameter representing solutions of perturbation theory problems.
Key words: S. A. Lomov’s regularization method, holomorphic regularization, pseudo-analyticity, $\varepsilon$-regular solution, $\varepsilon$-pseudo-regular solution.
Funding agency Grant number
Russian Science Foundation 23-21-00496
This work was supported by the Russian Science Foundation, project no. 23-21-00496.
Received: 27.03.2023
Revised: 27.03.2023
Accepted: 25.07.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 11, Pages 1996–2004
DOI: https://doi.org/10.1134/S096554252311012X
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: V. I. Kachalov, D. A. Maslov, “Analyticity and pseudo-analyticity in the small parameter method”, Zh. Vychisl. Mat. Mat. Fiz., 63:11 (2023), 1806–1814; Comput. Math. Math. Phys., 63:11 (2023), 1996–2004
Citation in format AMSBIB
\Bibitem{KacMas23}
\by V.~I.~Kachalov, D.~A.~Maslov
\paper Analyticity and pseudo-analyticity in the small parameter method
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 11
\pages 1806--1814
\mathnet{http://mi.mathnet.ru/zvmmf11643}
\crossref{https://doi.org/10.31857/S0044466923110170}
\elib{https://elibrary.ru/item.asp?id=54720586}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 11
\pages 1996--2004
\crossref{https://doi.org/10.1134/S096554252311012X}
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