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

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.

We are now preparing a paper on the weak approximation of such problem

References in corpus (4)

• An exponential integrator scheme for time discretization of nonlinear stochastic wave equation
• Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise
• Error estimates of finite element method for semi-linear stochastic strongly damped wave equation
• Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise

Cited by in corpus (5)

• Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations
• Exponential Integrators for Stochastic Maxwell's Equations Driven by Itô Noise
• Error estimates of finite element method for semi-linear stochastic strongly damped wave equation
• Hilbert--Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations
• Strong convergence rates for a full discretization of stochastic wave equation with nonlinear damping