A trigonometric method for the linear stochastic wave equation
This work provides a more efficient temporal integrator for stochastic wave equations, benefiting researchers in computational stochastic PDEs by removing step size constraints.
The paper presents a fully discrete approximation for the linear stochastic wave equation using a finite element method in space and a stochastic trigonometric scheme in time, achieving error bounds independent of spatial discretization and avoiding step size restrictions. Numerical experiments confirm these properties.
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.