On stabilized integration for time-dependent PDEs

DOI10.1016/j.jcp.2006.11.013zbMath1119.65382OpenAlexW2093936696MaRDI QIDQ885992

B. P. Sommeijer, Jan G. Verwer

Publication date: 14 June 2007

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

Full work available at URL: https://ir.cwi.nl/pub/19974

zbMATH Keywords

stabilitynumerical integrationnumerical examplesdamped wave equationsadvection equationsRunge-Kutta-Chebyshev methodscoupled sound and heat flowreactive flow problemsstabilized explicit integration

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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 first-order hyperbolic systems (35L45)

Related Items

PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise, Implicit-explicit predictor-corrector schemes for nonlinear parabolic differential equations, Second-order stabilized explicit Runge-Kutta methods for stiff problems, Kronecker product splitting preconditioners for implicit Runge-Kutta discretizations of viscous wave equations, Optimized low-dispersion and low-dissipation two-derivative Runge-Kutta method for wave equations, Runge-Kutta methods and viscous wave equations

Uses Software

• IRKC
• RKC

Cites Work

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• Modeling low Mach number reacting flow with detailed chemistry and transport
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• Runge-Kutta-Chebyshev projection method
• Convergence properties of the Runge-Kutta-Chebyshev method
• RKC: An explicit solver for parabolic PDEs
• Explicit difference schemes for solving stiff problems with a complex or separable spectrum
• IRKC: an IMEX solver for stiff diffusion-reaction PDEs
• On the Internal Stability of Explicit,m-Stage Runge-Kutta Methods for Largem-Values
• On Maxwell's Equations in an Electromagnetic Field with the Temperature Effect
• An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
• von Neumann stability conditions for the convection-diffusion eqation
• Second order Chebyshev methods based on orthogonal polynomials
• Explicit Runge-Kutta methods for parabolic partial differential equations