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This paper is concerned with the strong approximation of a semi-linearstochastic wave equation with strong damping, driven by additive noise. Basedon a spatial discretization performed by a spectral Galerkin method, weintroduce a kind of accelerated exponential time integrator involving linearfunctionals of the noise. Under appropriate assumptions, we provide errorbounds for the proposed full-discrete scheme. It is shown that the schemeachieves higher strong order in time direction than the order of temporalregularity of the underlying problem, which allows for higher convergence ratethan usual time-stepping schemes. For the space-time white noise case in two orthree spatial dimensions, the scheme still exhibits a good convergenceperformance. Another striking finding is that, even for the velocity with lowregularity the scheme always promises first order strong convergence in time.Numerical examples are finally reported to confirm our theoretical findings.

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