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A fully discrete approximation of the one-dimensional stochastic wave equation
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Universitat Autònoma de Barcelona.
2016 (English)In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, Vol. 36, no 1, 400-420 p.Article in journal (Refereed) Published
Abstract [en]

A fully discrete approximation of one-dimensional nonlinear stochastic wave equations driven by multiplicative noise is presented. A standard finite difference approximation is used in space and a stochastic trigonometric method is used for the temporal approximation. This explicit time integrator allows for error bounds in Lp(Ω)" style="position: relative;" tabindex="0" id="MathJax-Element-1-Frame" class="MathJax">Lp(Ω), uniformly in time and space, in such a way that the time discretization does not suffer from any kind of CFL-type step-size restriction. Moreover, uniform almost sure convergence of the numerical solution is also proved. Numerical experiments are presented and confirm the theoretical results.

Place, publisher, year, edition, pages
Oxford University Press, 2016. Vol. 36, no 1, 400-420 p.
Keyword [en]
nonlinear stochastic wave equation, multiplicative noise, strong convergence, finite differences, ochastic trigonometric methods
National Category
Computational Mathematics
URN: urn:nbn:se:umu:diva-99204DOI: 10.1093/imanum/drv006ISI: 000371150600016OAI: diva2:786090
Swedish Research Council, 2013-4562
Available from: 2015-02-04 Created: 2015-02-04 Last updated: 2016-04-15Bibliographically approved

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