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Mathematics of Computation

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Analysis of splitting methods for reaction-diffusion problems using stochastic calculus

Author: Erwan Faou
Journal: Math. Comp. 78 (2009), 1467-1483
MSC (2000): Primary 65M15, 60H30, 65C05
Published electronically: November 6, 2008
MathSciNet review: 2501058
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Abstract: We consider linear and nonlinear reaction-diffusion problems, and their time discretization by splitting methods. We give probabilistic interpretations of the splitting schemes, and show how these representations allow us to give error bounds for the deterministic propagator under weak hypothesis on the reaction part. To show these results, we only use the Itô formula, and basic properties of solutions of stochastic differential equations. Eventually, we show how probabilistic representations of splitting schemes can be used to derive ``hybrid'' numerical schemes based on Monte Carlo approximations of the splitting method itself.

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Additional Information

Erwan Faou
Affiliation: INRIA & Ecole Normale Supérieure de Cachan Bretagne, Avenue Robert Schumann, 35170 Bruz, France

Keywords: Splitting methods, reaction-diffusion equations, stochastic processes, Monte Carlo methods
Received by editor(s): November 13, 2007
Received by editor(s) in revised form: May 13, 2008
Published electronically: November 6, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.