Numerical Solution to the Multi-Term Time Fractional Diffusion Equation in a Finite Domain

被引：34
|
作者：
Li, Gongsheng [1 ]
Sun, Chunlong [1 ]
Jia, Xianzheng [1 ]
Du, Dianhu [1 ]
机构：
[1] Shandong Univ Technol, Sch Sci, Zibo 255049, Shandong, Peoples R China
来源：
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2016年 / 9卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Multi-term time fractional diffusion; finite difference scheme; spectral radius; stability and convergence; numerical simulation; BOUNDARY-VALUE-PROBLEMS; VARIABLE-ORDER; POROUS-MEDIA; DISPERSION; TRANSPORT; OPERATORS;
D O I：
10.4208/nmtma.2016.y13024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with numerical solution to the multi-term time fractional diffusion equation in a finite domain. An implicit finite difference scheme is established based on Caputo's definition to the fractional derivatives, and the upper and lower bounds to the spectral radius of the coefficient matrix of the difference scheme are estimated, with which the unconditional stability and convergence are proved. The numerical results demonstrate the effectiveness of the theoretical analysis, and the method and technique can also be applied to other kinds of time/space fractional diffusion equations.
引用
收藏
页码：337 / 357
页数：21
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