The time discretization of stochastic fractional wave equation is studied by using difference methods. Firstly, we use the rectangular formula to obtain a low-order time discretization, and its strong convergence order is less than 1 in the sense of mean squared $L^2$-norm. Meanwhile, by modifying the low order method with trapezoidal rule, the convergence rate is improved at expenses of requiring some extra temporal regularity to the solution. The modified scheme has superlinear convergence rate under the mean squared $L^2$-norm. Several numerical experiments are provided to confirm the theoretical error estimates.

中文翻译：

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谱分数随机波动方程时间离散的差分方法

采用差分方法研究了随机分数波动方程的时间离散化。首先，我们使用矩形公式得到一个低阶时间离散化，其强收敛阶在均方意义上小于1${\mathrm{大号}}^2$-规范。同时，通过对梯形规则的低阶方法进行修改，提高了收敛速度，但代价是对解需要一些额外的时间规律性。修改后的方案在均方下具有超线性收敛速度${\mathrm{大号}}^2$-规范。提供了几个数值实验来确认理论误差估计。