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

Peter Kloeden; Gabriel Lord; Andreas  Neuenkirch; Tony Shardlow

doi:10.1016/j.cam.2010.08.011

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

Peter Kloeden, Gabriel Lord, Andreas Neuenkirch, Tony Shardlow

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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 language	English
Pages (from-to)	1245–1260
Number of pages	16
Journal	Journal of Computational and Applied Mathematics
Volume	235
Issue number	5
DOIs	https://doi.org/10.1016/j.cam.2010.08.011
Publication status	Published - 1 Jan 2011

Keywords

stochastic PDE
numerical analysis
reaction-diffusion

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10.1016/j.cam.2010.08.011

Author's version
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
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Cite this

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AU - Lord, Gabriel

AU - Neuenkirch, Andreas

AU - Shardlow, Tony

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N2 - 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).

AB - 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).

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KW - numerical analysis

KW - reaction-diffusion

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ER -

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

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Keywords

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