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arXiv · 1203.3668

A trigonometric method for the linear stochastic wave equation

D. Cohen·S. Larsson·M. Sigg
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Abstract

A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretisation and a stochastic trigonometric scheme for the temporal approximation. This explicit time integrator allows for error bounds independent of the space discretisation and thus do not have a step size restriction as in the often used St\"ormer-Verlet-leap-frog scheme. Moreover it enjoys a trace formula as does the exact solution of our problem. These favourable properties are demonstrated with numerical experiments.

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D. Cohen, S. Larsson, M. Sigg. 2012-03-16. A trigonometric method for the linear stochastic wave equation. https://doi.org/10.1137/12087030x

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