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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.

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    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
    CreatorsKloeden, P., Lord, G., Neuenkirch, A. and Shardlow, T.
    DOI10.1016/j.cam.2010.08.011
    Uncontrolled Keywordsstochastic pde, numerical analysis, reaction-diffusion
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher Statementspde_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
    RefereedYes
    StatusPublished
    ID Code32124

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