A numerical scheme for stochastic PDEs with Gevrey regularity

Gabriel J. Lord, Jacques Rougemont

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

We consider strong approximations to parabolic stochastic PDEs. We assume the noise lies in a Gevrey space of analytic functions. This type of stochastic forcing includes the case of forcing in a finite number of Fourier modes. We show that with Gevrey noise our numerical scheme has solutions in a discrete equivalent of this space and prove a strong error estimate. Finally we present some numerical results for a stochastic PDE with a Ginzburg-Landau nonlinearity and compare this to the more standard implicit Euler-Maruyama scheme.

Original languageEnglish
Pages (from-to)587-604
Number of pages18
JournalIMA Journal of Numerical Analysis
Volume24
Issue number4
DOIs
Publication statusPublished - Oct 2004

Keywords

  • Gevrey regularity
  • Stochastic partial differential equations
  • Strong error estimate

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