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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 1, Pages 102–111
DOI: https://doi.org/10.31857/S0044466923010040 (Mi zvmmf11500) 		 
Partial Differential Equations

Convergence of formal solutions to the second member of the fourth Painlevé hierarchy in a neighborhood of zero

V. I. Anoshin, A. D. Beketova, A. V. Parusnikova, E. D. Prokopenko

National Research University – Higher School of Economics, 123458, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466923010040
Abstract: The second member of the fourth Painlevé hierarchy is considered. Convergence of certain power asymptotic expansions in a neighborhood of zero is proved. New families of power asymptotic expansions are found. Computations are carried out using a computer algebra system. Reference to a code that can be used for computing the Gevrey order of the formal expansion of the solution to the second-order differential equation in a symbolic computation packet is given.
Key words: asymptotic expansions, Gevrey orders, Painlevé equations, symbolic computations.
Funding agency Grant number
Russian Science Foundation 19-71-10003
This work was supported by the Russian Science Foundation, grant no. 19-71-10003, https://rscf.ru/en/project/19-71-10003/.
Received: 04.08.2022
Revised: 04.08.2022
Accepted: 10.09.2022
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 1, Pages 86–95
DOI: https://doi.org/10.1134/S0965542523010049
Bibliographic databases:
Document Type: Article
UDC: 517.928
Language: Russian
Citation: V. I. Anoshin, A. D. Beketova, A. V. Parusnikova, E. D. Prokopenko, “Convergence of formal solutions to the second member of the fourth Painlevé hierarchy in a neighborhood of zero”, Zh. Vychisl. Mat. Mat. Fiz., 63:1 (2023), 102–111; Comput. Math. Math. Phys., 63:1 (2023), 86–95
Citation in format AMSBIB
\Bibitem{AnoBekPar23}
\by V.~I.~Anoshin, A.~D.~Beketova, A.~V.~Parusnikova, E.~D.~Prokopenko
\paper Convergence of formal solutions to the second member of the fourth Painlev\'e hierarchy in a neighborhood of zero
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 1
\pages 102--111
\mathnet{http://mi.mathnet.ru/zvmmf11500}
\crossref{https://doi.org/10.31857/S0044466923010040}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4572162}
\elib{https://elibrary.ru/item.asp?id=50404572}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 1
\pages 86--95
\crossref{https://doi.org/10.1134/S0965542523010049}
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