Higher order time discretization for the stochastic semilinear wave equation with multiplicative noise

TL;DR

This paper introduces a higher-order time discretization scheme for the stochastic semilinear wave equation with multiplicative noise, achieving improved convergence order through variational analysis and computational validation.

Contribution

It develops a novel higher-order discretization method with proven convergence order of 3/2 for stochastic wave equations with multiplicative noise.

Findings

Convergence order of 3/2 demonstrated

Holder continuity and moment bounds established

Computational experiments confirm theoretical results

Abstract

In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ a variational method for its error analysis and prove an improved convergence order of 3/2 for the approximates of the solution. The core of the analysis is Holder continuity in time and moment bounds for the solutions of the continuous and the discrete problem. Computational experiments are also presented.