Essentially optimal explicit Runge-Kutta methods with application to hyperbolic-parabolic equations

DOI10.1007/s00211-006-0059-5zbMath1113.65074OpenAlexW2003713229MaRDI QIDQ879922

Manuel Torrilhon, Rolf Jeltsch

Publication date: 10 May 2007

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

Full work available at URL: https://doi.org/10.1007/s00211-006-0059-5

zbMATH Keywords

stabilityadvection-diffusion equationsemi-discretizationsnumerical experiments

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) PDEs of mixed type (35M10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) 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)

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Uses Software

• RKC
• RODAS

Cites Work

• RKC time-stepping for advection-diffusion-reaction problems
• Stability of explicit time discretizations for solving initial value problems
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• Some stability results for explicit Runge-Kutta methods
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• Solving Ordinary Differential Equations I
• On the Internal Stability of Explicit,m-Stage Runge-Kutta Methods for Largem-Values
• Largest disk of stability of explicit Runge-Kutta methods
• Finite Volume Methods for Hyperbolic Problems
• Two‐Dimensional Bulk Microflow Simulations Based on Regularized Grad’s 13‐Moment Equations
• Geometric multigrid with applications to computational fluid dynamics
• Second order Chebyshev methods based on orthogonal polynomials
• Explicit Runge-Kutta methods for parabolic partial differential equations
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