A variable time-step-size code for advection-diffusion-reaction PDEs

DOI10.1016/j.apnum.2012.06.024zbMath1259.65137OpenAlexW1995359357MaRDI QIDQ450907

S. Pérez-Rodríguez, S. González-Pinto

Publication date: 26 September 2012

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.06.024

zbMATH Keywords

stabilityinitial value problemsapproximate matrix factorizationsemidiscretizationfinite differenceembedded pairsadvection-diffusion-reaction equationlocal error estimateradiation-diffusion problemsRunge-Kutta Radau IIA methodsingle-Newton iteration

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) 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 (7)

Splitting-methods based on approximate matrix factorization and Radau-IIA formulas for the time integration of advection diffusion reaction PDEs ⋮ High-performance computation of pricing two-asset American options under the Merton jump-diffusion model on a GPU ⋮ W-methods to stabilize standard explicit Runge-Kutta methods in the time integration of advection-diffusion-reaction PDEs ⋮ A family of three-stage third order AMF-W-methods for the time integration of advection diffusion reaction PDEs. ⋮ A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems ⋮ Rosenbrock-type methods with inexact AMF for the time integration of advection-diffusion-reaction PDEs ⋮ AMF-Runge-Kutta formulas and error estimates for the time integration of advection diffusion reaction PDEs

Uses Software

• IRKC
• RKC
• RODAS
• LSODA

Cites Work

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• RKC time-stepping for advection-diffusion-reaction problems
• A study of B-convergence of Runge-Kutta methods
• Reduced storage matrix methods in stiff ODE systems
• RKC: An explicit solver for parabolic PDEs
• Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
• Runge-Kutta methods for the numerical solution of stiff semilinear systems
• An iterated Radau method for time-dependent PDEs
• IRKC: an IMEX solver for stiff diffusion-reaction PDEs
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• An Attempt to Avoid Exact Jacobian and Nonlinear Equations in the Numerical Solution of Stiff Differential Equations
• An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
• Approximate factorization for time-dependent partial differential equations

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