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

Erwan Faou 1, 2
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We consider linear and nonlinear reaction-diffusion problems, and their time dis- cretization by splitting methods. We give probabilistic interpretations of the splitting schemes, and show how these representations allow to give error bounds for the deter- ministic propagator under weak hypothesis on the reaction part. To show these results, we only use the Itˆo 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 approxima- tions of the splitting method itself.
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https://hal.inria.fr/hal-00777649
Contributor : Erwan Faou <>
Submitted on : Thursday, January 17, 2013 - 5:08:04 PM
Last modification on : Friday, February 5, 2021 - 3:49:00 AM

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  • HAL Id : hal-00777649, version 1

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Erwan Faou. Analysis of splitting methods for reaction-diffusion problems using stochastic calculus. Mathematics of Computation, American Mathematical Society, 2009, 78, pp.1467-1483. ⟨hal-00777649⟩

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