Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces

DOI10.1016/j.jcp.2017.04.071zbMath1380.65059OpenAlexW2610845878MaRDI QIDQ1693883

J. A. C. Weideman, Bengt Fornberg, Marco Fasondini

Publication date: 1 February 2018

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://scholar.colorado.edu/downloads/z316q270t

zbMATH Keywords

Padé approximationPainlevé transcendentsRiemann surfaceP\(_{\mathrm{III}}\) equationP\(_{\mathrm{V}}\) equationP\(_{\mathrm{VI}}\) equation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05)

Related Items (6)

Open problems for Painlevé equations ⋮ Numerical approach to Painlevé transcendents on unbounded domains ⋮ Special function solutions of Painlevé equations: theory, asymptotics and applications ⋮ A computational exploration of the McCoy-Tracy-Wu solutions of the third Painlevé equation ⋮ Asymptotic expansions relating to the distribution of the length of longest increasing subsequences ⋮ On the quasi-Ablowitz–Segur and quasi-Hastings–McLeod solutions of the inhomogeneous Painlevé II equation

Uses Software

• DLMF
• Differentiation Matrix Suite

Cites Work

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