Volume 52, pp. 77-87, 2020.

Leap-frog method for stochastic functional wave equations

Henryk Leszczyński, Milena Matusik, and Monika Wrzosek

Abstract

We perform a time-space discretisation, known as the leap-frog method, for nonlinear stochastic functional wave equations driven by multiplicative time-space white noise. To prove its stability we apply Cairoli's maximal inequalities for two-parameter martingales and provide a lemma for estimating solutions to a class of stochastic wave equations and a Gronwall-type inequality over cones. The method converges in $L^2$ at a rate of $O(\sqrt{h})$, where $h$ is a time-space step size.

Full Text (PDF) [385 KB], BibTeX , DOI: 10.1553/etna_vol52s77

Key words

leap-frog, stochastic wave equation

AMS subject classifications

60H15, 35R60, 35R10