The exponential integrator scheme for stochastic partial differential equations: pathwise error bounds

Peter Kloeden, Gabriel Lord, Andreas Neuenkirch, Tony Shardlow

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)
119 Downloads (Pure)

Abstract

We present an error analysis for a general semilinear stochastic evolution equation in d dimensions based on pathwise approximation. We discretize in space by a Fourier Galerkin method and in time by a stochastic exponential integrator. We show that for spatially regular (smooth) noise the number of nodes needed for the noise can be reduced and that the rate of convergence degrades as the regularity of the noise reduces (and the noise is rougher).
Original languageEnglish
Pages (from-to)1245–1260
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume235
Issue number5
DOIs
Publication statusPublished - 1 Jan 2011

Keywords

  • stochastic PDE
  • numerical analysis
  • reaction-diffusion

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