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In this paper, we present an energy-preserving exponentially integrablenumerical method for stochastic wave equation with cubic nonlinearity andadditive noise. We first apply the spectral Galerkin method to discretizing theoriginal equation and show that this spatial discretization possesses an energyevolution law and certain exponential integrability property. Then theexponential integrability property of the exact solution is deduced by provingthe strong convergence of the semi-discretization. To propose a full discretenumerical method which could inherit both the energy evolution law and theexponential integrability, we use the splitting technique and averaged vectorfield method in the temporal direction. Combining these structure-preservingproperties with regularity estimates of the exact and the numerical solutions,we obtain the strong convergence rate of the numerical method. Numericalexperiments coincide with these theoretical results.

Energy-preserving exponential integrable numerical method for stochastic cubic wave equation with additive noise