On the numerical solution to a nonlinear wave equation associated with the first Painlevé equation: an operator-splitting approach

DOI10.1007/s11401-013-0764-1zbMath1268.65112OpenAlexW2134748817MaRDI QIDQ1951207

Annalisa Quaini, Roland Glowinski

Publication date: 29 May 2013

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-013-0764-1

zbMATH Keywords

finite difference methodPainlevé equationnumerical experimentsnonlinear wave equationblow-up solutionsemidiscretizationoperator-splittingGalerkin/finite element space approximation

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Uses Software

• DLMF

Cites Work

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• Monodromy problem and the boundary condition for some Painlevé equations
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• An operator splitting scheme with a distributed Lagrange multiplier based fictitious domain method for wave propagation problems
• Numerical methods for a class of nonlinear integro-differential equations
• On solutions of nonlinear wave equations
• ON THE CONNECTION FORMULAS OF THE FOURTH PAINLEVÉ TRANSCENDENT
• Numerical Methods Based on Additive Splittings for Hyperbolic Partial Differential Equations
• Rates of Convergence for Viscous Splitting of the Navier-Stokes Equations
• On the Construction and Comparison of Difference Schemes

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