Runge-Kutta methods and viscous wave equations

DOI10.1007/s00211-009-0211-0zbMath1167.65052OpenAlexW2158880086MaRDI QIDQ1027735

Jan G. Verwer

Publication date: 30 June 2009

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-009-0211-0

zbMATH Keywords

numerical examplesmethod of linessemidiscretizationRunge-Kutta methods\(A\)-stabilityviscous wave equations

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (7)

Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations ⋮ Unified compact ADI methods for solving nonlinear viscous and nonviscous wave equations ⋮ The study of a fourth-order multistep ADI method applied to nonlinear delay reaction-diffusion equations ⋮ High-order finite difference methods for a second order dual-phase-lagging models of microscale heat transfer ⋮ Doubly nonlinear evolution equations of second order: existence and fully discrete approximation ⋮ Kronecker product splitting preconditioners for implicit Runge-Kutta discretizations of viscous wave equations ⋮ Analysis and application of a compact multistep ADI solver for a class of nonlinear viscous wave equations

Uses Software

• RODAS

Cites Work

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• Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems
• Absolute monotonicity of polynomials occuring in the numerical solution of initial value problems
• Solving Ordinary Differential Equations I
• Highest possible order of algebraically stable diagonally implicit runge-kutta methods
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• A stability property of implicit Runge-Kutta methods
• Stability Criteria for Implicit Runge–Kutta Methods
• Numerical Solution of Ordinary Differential Equations
• Multirate Time Stepping for Stiff ODEs
• A special stability problem for linear multistep methods
• Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Erhard Schmidt zum 75. Geburtstag in Verehrung gewidmet
• Iterative solution and finite difference approximations to 3D microscale heat transport equation

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