A trigonometric method for the linear stochastic wave equation
Preprint, 2012

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 Störmer-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.

Additive noise

Stochastic trigonometric schemes

Geometric numerical integration

Trace formula

Strong convergence

Stochastic wave equation

Författare

David Cohen

Stig Larsson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Magdalena Sigg

arXiv

antal sidor: 18-

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper