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Convergence of a splitting method of high order for reaction-diffusion systems

Author: Stéphane Descombes
Journal: Math. Comp. 70 (2001), 1481-1501
MSC (2000): Primary 65M12, 65B05, 65J15
Published electronically: July 11, 2000
MathSciNet review: 1836914
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In this article, we prove the convergence of a splitting scheme of high order for a reaction-diffusion system of the form $u_t-M\Delta u +F(u)=0$ where $M$ is an $m \times m$ matrix whose spectrum is included in $\{{\mathfrak{R}} z > 0 \}$. This scheme is obtained by applying a Richardson extrapolation to a Strang formula.

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Additional Information

Stéphane Descombes
Affiliation: Unité de Mathématiques Pures et Appliquées, CNRS UMR 5669, Ecole Normale Supérieure de Lyon, 46, Allée d’Italie, 69364 Lyon Cedex 07, France

Keywords: Splitting, reaction-diffusion systems
Received by editor(s): November 10, 1998
Received by editor(s) in revised form: November 29, 1999
Published electronically: July 11, 2000
Article copyright: © Copyright 2000 American Mathematical Society