Analysis of the L1 scheme for fractional wave equations with nonsmooth data

被引：9
作者：
Li, Binjie [1 ]
Wang, Tao [2 ]
Xie, Xiaoping [1 ]
机构：
[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China
[2] South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 90卷
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Fractional wave equation; L1; scheme; Stability; Convergence; Nonsmooth data; DISCONTINUOUS GALERKIN METHOD; EVOLUTION EQUATION; DIFFUSION; DISCRETIZATION; APPROXIMATIONS; SUPERCONVERGENCE; STABILITY; FORMULA;
D O I：
10.1016/j.camwa.2021.03.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper analyzes the well-known L1 scheme for fractional wave equations with nonsmooth data. A new stability estimate and temporal accuracy O(tau(3-alpha)) are obtained. In addition, a modified L1 scheme is proposed, and its stability and temporal accuracy O(tau(2)) 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.
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页码：1 / 12
页数：12
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