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.

提出了分别由加性和乘性噪声驱动的随机空间分数非线性阻尼波方程的全离散新方案。基于通过四阶中心差分方案完成的空间离散化，开发了半隐式Crank-Nicolson方案进行时间逼近。给出了加性噪声和乘性Stratonovich噪声的能量跟踪公式。此外，所观察到的数值方案的离散能量跟踪公式与理论分析结果的行为是一致的。否则，计算数值方案在时间上的收敛性。最后进行了一些数值实验以验证理论在长时间的计算中。