New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation

被引：319
|
作者：
Zhuang, P. [1 ]
Liu, F. [2 ,3 ]
Anh, V. [2 ]
Turner, I. [2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361006, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
[3] S China Univ Technol, Sch Math Sci, Guangzhou 510640, Guangdong, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 46卷 / 02期
关键词：
anomalous subdiffusion equation; implicit numerical method; stability; convergence; fractional integro-differential equation;
D O I：
10.1137/060673114
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous subdiffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and convergence of the INM are investigated by the energy method. Some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and supporting theoretical results can also be applied to other fractional integro-differential equations and higher-dimensional problems.
引用
收藏
页码：1079 / 1095
页数：17
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