Painlevé IV with both Parameters Zero: A Numerical Study

DOI10.1111/j.1467-9590.2012.00564.xzbMath1271.34090OpenAlexW1573187633MaRDI QIDQ4917506

Jonah A. Reeger, Bengt Fornberg

Publication date: 30 April 2013

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

Full work available at URL: https://doi.org/10.1111/j.1467-9590.2012.00564.x

zbMATH Keywords

Painlevé IV equationnumerical studypole locations

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (11)

Addendum: Painlevé transcendents and PT -symmetric Hamiltonians (2015 J. Phys. A: Math. Theor. 48 475202) ⋮ A dynamical systems approach to the fourth Painlevé equation ⋮ Singular asymptotics for the Clarkson-McLeod solutions of the fourth Painlevé equation ⋮ Open problems for Painlevé equations ⋮ A computational overview of the solution space of the imaginary Painlevé II equation ⋮ A computational exploration of the McCoy-Tracy-Wu solutions of the third Painlevé equation ⋮ Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces ⋮ A computational exploration of the second Painlevé equation ⋮ A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI ⋮ Painlevé IV: A numerical study of the fundamental domain and beyond ⋮ A method for calculating the Painlevé transcendents

Uses Software

• DLMF

Cites Work

• Unnamed Item
• A general framework for solving Riemann-Hilbert problems numerically
• A numerical methodology for the Painlevé equations
• Correlations of RMT characteristic polynomials and integrability: Hermitean matrices
• Padé approximations for Painlevé I and II transcendents
• Fredholm determinants, differential equations and matrix models
• Replica Field Theories, Painlevé Transcendents, and Exact Correlation Functions
• Integral equations and exact solutions for the fourth Painlevé equation
• Numerical studies of the fourth Painlevé equation
• Connection formulae for the fourth Painlevé transcendent; Clarkson-McLeod solution
• A new integration algorithm for ordinary differential equations based on continued fraction approximations
• The fourth Painlevé equation and associated special polynomials
• Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.

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