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

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 variational method for its error analysis and prove an improved convergence order of [Formula presented] for the approximates of the solution. The core of the analysis is H�lder continuity in time and moment bounds for the solutions of the continuous and the discrete problem. Computational experiments are also presented. � The Author(s) 2023. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.