A Trigonometric Method for the Linear Stochastic Wave Equation
Artikel i vetenskaplig tidskrift, 2013

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 discretization and a stochastic trigonometric scheme for the temporal approximation. This explicit time integrator allows for error bounds independent of the space discretization and thus does 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 favorable properties are demonstrated with numerical experiments.

Additive noise

Strong convergence

Stochastic wave equation

Trace formula

Geometric numerical integration

Stochastic trigonometric schemes

Författare

David Cohen

Karlsruher Institut für Technologie (KIT)

Umeå universitet

Stig Larsson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Magdalena Sigg

Universität Basel

SIAM Journal on Numerical Analysis

0036-1429 (ISSN) 1095-7170 (eISSN)

Vol. 51 1 204-222

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

DOI

10.1137/12087030X