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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 3, Pages 379–387 (Mi zvmmf9667)  
This article is cited in 8 scientific papers (total in 8 papers)

Numerical solution of the Cauchy problem for the Painlevé; I and II equations

A. A. Abramova, L. F. Yukhnob

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047 Russia
Full-text PDF (268 kB) Citations (8)
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Abstract: A numerical method for solving the Cauchy problem for the first and second Painlevé; differential equations is proposed. The presence of movable poles of the solution is allowed. The positions of the poles are not a priori known and are determined in the process of solving the equation. The proposed method is based on the transition to an auxiliary system of differential equations in a neighborhood of a pole. The equations in this system and its solution have no singularities in either the pole or its neighborhood. Numerical results confirming the efficiency of this method are presented.
Key words: Painlevé I and II ordinary differential equations, pole of a solution, numerical method.
Received: 18.10.2011
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 3, Pages 321–329
DOI: https://doi.org/10.1134/S0965542512030025
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: A. A. Abramov, L. F. Yukhno, “Numerical solution of the Cauchy problem for the Painlevé; I and II equations”, Zh. Vychisl. Mat. Mat. Fiz., 52:3 (2012), 379–387; Comput. Math. Math. Phys., 52:3 (2012), 321–329
Citation in format AMSBIB
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    • This publication is cited in the following 8 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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