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

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**78**(2009), 1467-1483 Request permission

## 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.## References

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## Additional Information

**Erwan Faou**- Affiliation: INRIA & Ecole Normale Supérieure de Cachan Bretagne, Avenue Robert Schumann, 35170 Bruz, France
- MR Author ID: 656335
- Email: Erwan.Faou@inria.fr
- Received by editor(s): November 13, 2007
- Received by editor(s) in revised form: May 13, 2008
- Published electronically: November 6, 2008
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**78**(2009), 1467-1483 - MSC (2000): Primary 65M15, 60H30, 65C05
- DOI: https://doi.org/10.1090/S0025-5718-08-02185-6
- MathSciNet review: 2501058