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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2023 Volume 63, Number 1, Pages 102–111 (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

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.

UDC: 517.928

Received: 04.08.2022
Revised: 04.08.2022
Accepted: 10.09.2022

DOI: 10.31857/S0044466923010040


 English version:
Computational Mathematics and Mathematical Physics, 2023, 63:1, 86–95

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© Steklov Math. Inst. of RAS, 2026