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Analysis of the L1 scheme for fractional wave equations with nonsmooth data
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2021-03-23 , DOI: 10.1016/j.camwa.2021.03.006
Binjie Li , Tao Wang , Xiaoping Xie

This paper analyzes the well-known L1 scheme for fractional wave equations with nonsmooth data. A new stability estimate and temporal accuracy O(τ3α) are obtained. In addition, a modified L1 scheme is proposed, and its stability and temporal accuracy O(τ2) 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:

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Øτ3-α获得。另外,提出了一种改进的L1方案,其稳定性和时间精度Øτ2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。

更新日期:2021-03-23
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