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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:447

Article

Qi, Ruisheng¹  Wang, Xiaojie² 

[1] Northeastern Univ, Sch Math & Stat, Qinhuangdao, Peoples R China

[2] Cent S Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China

关键词: Strongly damped wave equation;    Infinite dimensional Wiener process;    Spectral Galerkin method;    Accelerated exponential time integrator;    Strong approximation;   

DOI  :  10.1016/j.jmaa.2016.09.052

来源: Elsevier

【 摘 要 】

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 fimctionals 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. Particularly 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free