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2006 On numerical solutions of the stochastic wave equation
John B. Walsh
Illinois J. Math. 50(1-4): 991-1018 (2006). DOI: 10.1215/ijm/1258059497

Abstract

We show that there is a numerical scheme for the stochastic wave equation which converges in $L^p$ at a rate of $O(\sqrt h)$, and which converges a.s. uniformly on compact sets at a rate $O(\sqrt{ h|\log h|^\ep})$\,, for any $\ep >0$\,, where $h$ is the step size in both time and space. We show that this is the optimal rate: there is no scheme depending on the same increments of white noise which has a higher order of convergence.

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John B. Walsh. "On numerical solutions of the stochastic wave equation." Illinois J. Math. 50 (1-4) 991 - 1018, 2006. https://doi.org/10.1215/ijm/1258059497

Information

Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1108.60058
MathSciNet: MR2247851
Digital Object Identifier: 10.1215/ijm/1258059497

Subjects:
Primary: 60H35
Secondary: 60H15, 65C30, 65M70

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign

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Vol.50 • No. 1-4 • 2006
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