An accelerated exponential time integrator for semi-linear stochastic strongly damped wave equation with additive noise

TL;DR

This paper introduces an accelerated exponential integrator for semi-linear stochastic wave equations with damping and additive noise, achieving higher convergence rates and effective performance even with low regularity noise.

Contribution

It proposes a novel accelerated exponential time integrator that improves convergence rates for stochastic wave equations with damping, surpassing traditional schemes.

Findings

Achieves higher strong order in time than the regularity of the problem.

Performs well for space-time white noise in 2D and 3D.

Guarantees first-order strong convergence for low-regularity velocity.

Abstract

This paper is concerned with the strong approximation of a semi-linear stochastic wave equation with strong damping, driven by additive noise. Based on a spatial discretization performed by a spectral Galerkin method, we introduce a kind of accelerated exponential time integrator involving linear functionals of the noise. Under appropriate assumptions, we provide error bounds for the proposed full-discrete scheme. It is shown that the scheme achieves higher strong order in time direction than the order of temporal regularity of the underlying problem, which allows for higher convergence rate than usual time-stepping schemes. For the space-time white noise case in two or three spatial dimensions, the scheme still exhibits a good convergence performance. Another striking finding is that, even for the velocity with low regularity the scheme always promises first order strong convergence in time. Numerical examples are finally reported to confirm our theoretical findings.