An efficient alternating direction implicit finite difference scheme for the three-dimensional time-fractional telegraph equation

被引：16
作者：
Yang X. [1 ]
Qiu W. [2 ]
Zhang H. [1 ]
Tang L. [1 ]
机构：
[1] School of Science, Hunan University of Technology, Zhuzhou, 412007, Hunan
[2] School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan
来源：
Computers and Mathematics with Applications | 2021年 / 102卷
基金：
中国国家自然科学基金;
关键词：
ADI finite difference method; L1; formula; Numerical experiment; Stability and convergence; Three-dimensional time-fractional telegraph equation;
D O I：
10.1016/j.camwa.2021.10.021
中图分类号：
学科分类号：
摘要：
In this work, an efficient alternating direction implicit (ADI) finite difference scheme is proposed to solve the three-dimensional time-fractional telegraph equation. The fully-discrete scheme is established via the L1 discrete formula in temporal direction and finite difference method in spatial direction. In order to reduce the computational cost of solving three-dimensional problems, an ADI algorithm is designed and applied. Then, via the energy method, we prove the stability and convergence of the scheme in L2 and H1 norms, respectively. Eventually, several numerical examples are given to validate the theoretical results. © 2021 Elsevier Ltd
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页码：233 / 247
页数：14
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