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.
Type de document :
Article dans une revue
Mathematics of Computation, American Mathematical Society, 2009, 78, pp.1467-1483
Liste complète des métadonnées

https://hal.inria.fr/hal-00777649
Contributeur : Erwan Faou <>
Soumis le : jeudi 17 janvier 2013 - 17:08:04
Dernière modification le : mardi 19 juin 2018 - 11:12:07

Identifiants

  • HAL Id : hal-00777649, version 1

Citation

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〉

Partager

Métriques

Consultations de la notice

349