AMF-Runge-Kutta formulas and error estimates for the time integration of advection diffusion reaction PDEs

DOI10.1016/j.cam.2015.03.048zbMath1317.65190arXiv1501.02641OpenAlexW2035134613MaRDI QIDQ2352294

S. González-Pinto, D. Hernández-Abreu, S. Pérez-Rodríguez

Publication date: 30 June 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.02641

zbMATH Keywords

stabilityconvergencenumerical examplefinite differencesapproximate matrix factorizationsemidiscretizationevolutionary advection-diffusion-reaction partial differential equationsRunge-Kutta Radau IIA methods

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (3)

Splitting-methods based on approximate matrix factorization and Radau-IIA formulas for the time integration of advection diffusion reaction PDEs ⋮ W-methods to stabilize standard explicit Runge-Kutta methods in the time integration of advection-diffusion-reaction PDEs ⋮ Alternating directions implicit integration in a general linear method framework

Uses Software

• IRKC
• RKC
• VODE
• LSODA

Cites Work

• Splitting-methods based on approximate matrix factorization and Radau-IIA formulas for the time integration of advection diffusion reaction PDEs
• A variable time-step-size code for advection-diffusion-reaction PDEs
• RKC time-stepping for advection-diffusion-reaction problems
• Stability of the method of lines
• A study of B-convergence of Runge-Kutta methods
• Reduced storage matrix methods in stiff ODE systems
• RKC: An explicit solver for parabolic PDEs
• Iterative schemes for three-stage implicit Runge-Kutta methods
• An iterated Radau method for time-dependent PDEs
• IRKC: an IMEX solver for stiff diffusion-reaction PDEs
• VODE: A Variable-Coefficient ODE Solver
• An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
• Tridiagonal Toeplitz matrices: properties and novel applications
• A class ofA-stable methods
• Approximate factorization for time-dependent partial differential equations
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