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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Analysis of splitting methods for reaction-diffusion problems using stochastic calculus
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by Erwan Faou PDF
Math. Comp. 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.
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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