The infinitesimal generator (fractional Laplacian) of a process obtained by subordinating a killed Brownian motion catches the power-law attenuation of wave propagation. This paper studies the numerical schemes for the stochastic wave equation with fractional Laplacian as the space operator, the noise term of which is an infinite dimensional Brownian motion or fractional Brownian motion (fBm). Firstly, we establish the regularity of the mild solution of the stochastic fractional wave equation. Then a spectral Galerkin method is used for the approximation in space, and the space convergence rate is improved by postprocessing the infinite dimensional Gaussian noise. In the temporal direction, when the time derivative of the mild solution is bounded in the sense of mean-squared \(L^p\)-norm, we propose a modified stochastic trigonometric method, getting a higher strong convergence rate than the existing results, i.e., the time convergence rate is bigger than 1. Particularly, for time discretization, the provided method can achieve an order of 2 at the expenses of requiring some extra regularity to the mild solution. The theoretical error estimates are confirmed by numerical experiments.

通过服从被杀死的布朗运动获得的过程的无穷小生成器（分数拉普拉斯算子）捕获了波传播的幂律衰减。本文研究分数阶拉普拉斯算子为空间算子的随机波动方程的数值格式，其噪声项为无限维布朗运动或分数布朗运动（fBm）。首先，我们建立了随机分数波方程的温和解的正则性。然后将频谱Galerkin方法用于空间逼近，并通过对无限维高斯噪声进行后处理来提高空间收敛速度。在时间方向上，当温和溶液的时间导数在均方\（L ^ p \）的意义上有界时-范数，我们提出了一种改进的随机三角函数方法，该方法具有比现有结果更高的强收敛速度，即时间收敛速度大于1。特别是对于时间离散化，所提供的方法可以在2阶处获得2阶。要求对温和解有一些额外规律性的费用。理论误差估计通过数值实验得到证实。