This paper analyzes the well-known L1 scheme for fractional wave equations with nonsmooth data. A new stability estimate and temporal accuracy $\mathcal{O}\left({\tau }^{3-\alpha }\right)$ are obtained. In addition, a modified L1 scheme is proposed, and its stability and temporal accuracy $\mathcal{O}\left({\tau }^2\right)$ are also derived under nonsmooth data. The convergence of the two schemes in the inhomogeneous case are also established. Finally, numerical experiments are performed to verify the theoretical results.

中文翻译：

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具有不光滑数据的分数阶波动方程的L1格式分析

本文分析了非光滑数据分数波方程的著名L1格式。新的稳定性估计和时间精度$\mathcal{Ø}（{\tau }^{3-\alpha }）$获得。另外，提出了一种改进的L1方案，其稳定性和时间精度$\mathcal{Ø}（{\tau }^{\mathrm{2个}}）$也是根据不平滑的数据得出的。还建立了两种方案在非均匀情况下的收敛性。最后，通过数值实验验证了理论结果。