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Novel fully discrete schemes are developed to numerically approximate asemilinear stochastic wave equation driven by additive space-time white noise.Spectral Galerkin method is proposed for the spatial discretization, andexponential time integrators involving linear functionals of the noise areintroduced for the temporal approximation. The resulting fully discrete schemesare very easy to implement and allow for higher strong convergence rate in timethan existing time-stepping schemes such as the Crank-Nicolson-Maruyama schemeand the stochastic trigonometric method. Particularly, it is shown that the newschemes achieve in time an order of $1- \epsilon$ for arbitrarily small$\epsilon >0$, which exceeds the barrier order $\frac{1}{2}$ established byWalsh. Numerical results confirm higher convergence rates and computationalefficiency of the new schemes.

Higher order strong approximations of semilinear stochastic wave equation with additive space-time white noise