A method for calculating the Painlevé transcendents

DOI10.1016/j.apnum.2014.05.002zbMath1326.65086OpenAlexW2007933866MaRDI QIDQ2343614

L. F. Yukhno, A. A. Abramov

Publication date: 6 May 2015

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2014.05.002

zbMATH Keywords

numerical methodmovable singular pointsPainlevé I--VI equations

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Numerical methods for initial value problems involving ordinary differential equations (65L05) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Painlevé-type functions (33E17)

Related Items (2)

Open problems for Painlevé equations ⋮ Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces

Cites Work

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• Numerical solution of Riemann-Hilbert problems: Painlevé II
• A numerical methodology for the Painlevé equations
• Padé approximations for Painlevé I and II transcendents
• Numerical solution of the Cauchy problem for Painlevé III
• Numerical solution of the Painlevé IV equation
• Numerical solution of the Painlevé V equation
• Numerical solution of the Painlevé VI equation
• Numerical solution of the Cauchy problem for the Painlevé I and II equations
• On Boutroux's Tritronquée Solutions of the First Painlevé Equation
• Painlevé IV with both Parameters Zero: A Numerical Study
• The Dirichlet boundary value problem for real solutions of the first Painlevé equation on segments in non-positive semi-axis

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