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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 11, Pages 2023–2032 (Mi zvmmf9753)  
This article is cited in 5 scientific papers (total in 5 papers)

Numerical solution of the Painlevé IV equation

A. A. Abramova, L. F. Yukhnob

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
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Abstract: A numerical method for solving the Cauchy problem for the fourth Painlevé equation is proposed. The difficulty of the problem is that the unknown function can have movable singular points of the pole type; moreover, the equation may have singularities at the points where the solution vanishes. The positions of poles and zeros of the solution are not a priori known and are determined in the process of solving the equation. The proposed method is based on the transition to auxiliary systems of differential equations in neighborhoods of the indicated points. The equations in these systems and their solutions have no singularities in the corresponding point and its neighborhood. Numerical results confirming the efficiency of this method are presented.
Key words: Painlevé IV ordinary differential equation, pole of a solution, singularity of an equation, numerical method.
Received: 05.04.2012
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 11, Pages 1565–1573
DOI: https://doi.org/10.1134/S0965542512110036
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: A. A. Abramov, L. F. Yukhno, “Numerical solution of the Painlevé IV equation”, Zh. Vychisl. Mat. Mat. Fiz., 52:11 (2012), 2023–2032; Comput. Math. Math. Phys., 52:11 (2012), 1565–1573
Citation in format AMSBIB
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    • This publication is cited in the following 5 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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