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A fully discrete approximation of the one-dimensional stochastic heat equationPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2018 (English)In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642Article in journal (Other academic) Epub ahead of print
##### Abstract [en]

##### Place, publisher, year, edition, pages

Oxford University Press, 2018.
##### Keywords [en]

stochastic heat equation, multiplicative noise, finite difference scheme, stochastic exponential integrator, Lq(Ω)-convergence
##### National Category

Computational Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-146948DOI: 10.1093/imanum/dry060OAI: oai:DiVA.org:umu-146948DiVA, id: diva2:1200352
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##### Note

##### In thesis

A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space–time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method is used for the temporal approximation. Observe that the proposed exponential scheme does not suffer from any kind of CFL-type step size restriction. When the drift term and the diffusion coefficient are assumed to be globally Lipschitz this explicit time integrator allows for error bounds in Lq(Ω)" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">Lq(Ω)Lq(Ω), for all q⩾2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">q⩾2q⩾2, improving some existing results in the literature. On top of this we also prove almost sure convergence of the numerical scheme. In the case of nonglobally Lipschitz coefficients, under a strong assumption about pathwise uniqueness of the exact solution, convergence in probability of the numerical solution to the exact solution is proved. Numerical experiments are presented to illustrate the theoretical results.

Originally included in thesis in manuscript form.

Available from: 2018-04-24 Created: 2018-04-24 Last updated: 2019-04-051. Exponential integrators for stochastic partial differential equations$(function(){PrimeFaces.cw("OverlayPanel","overlay1200403",{id:"formSmash:j_idt757:0:j_idt761",widgetVar:"overlay1200403",target:"formSmash:j_idt757:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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