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

Reference:

Kloeden, P., Lord, G., Neuenkirch, A. and Shardlow, T., 2011. The exponential integrator scheme for stochastic partial differential equations: pathwise error bounds. Journal of Computational and Applied Mathematics, 235 (5), 1245–1260.

Official URL:

http://dx.doi.org/10.1016/j.cam.2010.08.011

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).

Details

Item Type	Articles
Creators	Kloeden, P., Lord, G., Neuenkirch, A. and Shardlow, T.
DOI	10.1016/j.cam.2010.08.011
Uncontrolled Keywords	stochastic pde, numerical analysis, reaction-diffusion
Departments	Faculty of Science > Mathematical Sciences
Publisher Statement	spde_jcam.pdf: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, vol 235, issue 5, 2011, DOI 10.1016/j.cam.2010.08.011
Refereed	Yes
Status	Published
ID Code	32124

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