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

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Xiaojie Wang




Grundläggande vetenskaper

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