Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise
Preprint, 2015

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal approximation. This explicit time integrator allows for mean-square error bounds indepen- dent of the space discretisation and thus do not suffer from a step size restriction as in the often used Störmer-Verlet- leap-frog scheme. Furthermore, it satisfies an almost trace formula (i. e., a linear drift of the expected value of the energy of the problem). Numerical experiments are presented and confirm the theoretical results.

Multiplicative noise

Strong convergence

Trace formula

Semi-linear stochastic wave equation

Stochastic trigonometric methods

Geometric numerical integration


Rikard Anton

David Cohen

Stig Larsson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Xiaojie Wang

Subject Categories

Computational Mathematics


Basic sciences

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