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
引用
收藏
页码：233 / 247
页数：14
相关论文
共 50 条
[41]   Efficient finite difference method for two-dimensional diffusion equation in comb structure with fractional derivative boundary conditions [J].
Bu, Weiping ;
Xu, Xiaohong ;
Zhao, Yue .
INTERNATIONAL JOURNAL OF MODELING SIMULATION AND SCIENTIFIC COMPUTING, 2025, 16 (01)
[42]   A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model [J].
Qiu, Wenlin ;
Xu, Da ;
Guo, Jing ;
Zhou, Jun .
NUMERICAL ALGORITHMS, 2020, 85 (01) :39-58
[43]   A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model [J].
Wenlin Qiu ;
Da Xu ;
Jing Guo ;
Jun Zhou .
Numerical Algorithms, 2020, 85 :39-58
[44]   A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation [J].
Pradip Roul ;
Vikas Rohil .
Numerical Algorithms, 2022, 90 :1357-1387
[45]   An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations [J].
Liu, Zeting ;
Liu, Fawang ;
Zeng, Fanhai .
APPLIED NUMERICAL MATHEMATICS, 2019, 136 :139-151
[46]   A BDF2 ADI difference scheme for a three-dimensional nonlocal evolution equation with multi-memory kernels [J].
Zhou, Ziyi ;
Zhang, Haixiang ;
Yang, Xuehua .
COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (08)
[47]   Efficient second-order ADI difference schemes for three-dimensional Riesz space-fractional diffusion equations(R) [J].
Zhu, Chen ;
Zhang, Bingyin ;
Fu, Hongfei ;
Liu, Jun .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 98 :24-39
[48]   Sharp error estimate of a compact L1-ADI scheme for the two-dimensional time-fractional integro-differential equation with singular kernels [J].
Wang, Zhibo ;
Cen, Dakang ;
Mo, Yan .
APPLIED NUMERICAL MATHEMATICS, 2021, 159 :190-203
[49]   A stable three-level explicit spline finite difference scheme for a class of nonlinear time variable order fractional partial differential equations [J].
Moghaddam, B. P. ;
Machado, J. A. T. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (06) :1262-1269
[50]   Finite Element Scheme with H2N2 Interpolation for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation [J].
Zhang, Huiqin ;
Chen, Yanping ;
Zhou, Jianwei ;
Wang, Yang .
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2024, 16 (05) :1197-1222
12345