RKC: An explicit solver for parabolic PDEs

DOI10.1016/S0377-0427(97)00219-7zbMath0910.65067OpenAlexW1966775587MaRDI QIDQ1385052

B. P. Sommeijer, Lawrence F. Shampine, Jan G. Verwer

Publication date: 26 April 1998

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(97)00219-7

zbMATH Keywords

stabilitynumerical examplestime integrationgrid generationreaction-diffusion equationparabolic problemsRunge-Kutta formulas of Chebychev typeRunge-Kutta-Chebychev algorithm

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) 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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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Uses Software

• M3RK
• VODE
• RKSUITE
• RODAS
• IMPEX

Cites Work

• Convergence properties of the Runge-Kutta-Chebyshev method
• Automatic selection of the initial step size for an ODE solver
• A PI stepsize control for the numerical solution of ordinary differential equations
• A comparison of preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a high order finite element method
• Diagnosing Stiffness for Runge–Kutta Methods
• Practical Aspects of Interpolation in Runge-Kutta Codes
• VODE: A Variable-Coefficient ODE Solver
• An Implementation of a Class of Stabilized Explicit Methods for the Time Integration of Parabolic Equations
• On the Internal Stability of Explicit,m-Stage Runge-Kutta Methods for Largem-Values
• ODE solvers and the method of lines
• Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems
• Explicit Runge-Kutta methods for parabolic partial differential equations
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