A compact ADI Crank-Nicolson difference scheme for the two-dimensional time fractional subdiffusion equation

被引：1
|
作者：
Li, Mingzhu [1 ,2 ]
Ma, Qiang [3 ]
Ding, Xiaohua [1 ,3 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin, Heilongjiang, Peoples R China
[2] Qingdao Univ Technol, Sch Sci, Qingdao, Peoples R China
[3] Harbin Inst Technol Weihai, Dept Math, Weihai, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2018年 / 95卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Compact ADI scheme; Crank-Nicolson difference scheme; fractional subdiffusion equation; convergence; stability; NUMERICAL-SOLUTION; DIFFUSION; APPROXIMATIONS; ALGORITHM;
D O I：
10.1080/00207160.2017.1411590
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a compact alternating direction implicit (ADI) Crank-Nicolson difference scheme is proposed and analysed for the solution of two-dimensional time fractional subdiffusion equation. The Riemann-Liouville time fractional derivative is approximated by the weighted and shifted Grunwald difference operator and the spatial derivative is discretized by a fourth-order compact finite difference method. The stability and convergence of the difference scheme are discussed and theoretically proven by using the energy method. Finally, numerical experiments are carried out to show that the numerical results are in good agreement with the theoretical analysis.
引用
收藏
页码：2525 / 2538
页数：14
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