Abstract
A new fully discrete scheme of stochastic space-fractional nonlinear damped wave equations respectively driven by additive and multiplicative noise is presented. Based on the spatial discretization done via a fourth-order central difference scheme, the semi-implicit Crank–Nicolson scheme is developed for the temporal approximation. The trace formulas for the energy are given for both additive noise and multiplicative Stratonovich noise. Furthermore, the discrete energy trace formula of numerical scheme observed is consistent with behavior of theoretical analysis results. Otherwise, the convergence of order for numerical scheme in time is calculated. Some numerical experiments are performed to verify theory in long time computations at last.
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