IMEX Runge-Kutta schemes for reaction-diffusion equations

By Toshiyuki Koto. 2008

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A fundamental research is carried out into convergence and stability properties of IMEX (implicit-explicit) Runge-Kutta schemes applied to reaction-diffusion equations. It is shown that a fully discrete scheme converges if it satisfies certain conditions using a technique of the B-convergence analysis, developed by Burrage, Hundsdorfer and Verwer in 1986. Stability of the schemes is also examined on the basis of a scalar test equation, proposed by Frank, Hundsdorfer and Verwer in 1997.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/412f7f1b4b7f22bf5093895b4bbd1bf56645ec93