Numerical simulation for the three-dimension fractional sub-diffusion equation

被引：31
|
作者：
Chen, J. [1 ]
Liu, F. [2 ]
Liu, Q. [3 ]
Chen, X. [1 ]
Anh, V. [2 ]
Turner, I. [2 ]
Burrage, K. [2 ,4 ,5 ]
机构：
[1] Jimei Univ, Sch Sci, Xiamen 361005, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
[3] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[4] Univ Oxford, COMLAB, Oxford OX1 3QD, England
[5] Univ Oxford, OCISB, Oxford OX1 3QD, England
来源：
APPLIED MATHEMATICAL MODELLING | 2014年 / 38卷 / 15-16期
基金：
中国国家自然科学基金;
关键词：
Three-dimensional fractional sub-diffusion equation; Fractional alternating direction implicit scheme; Stability; Convergence; DIFFERENCE APPROXIMATION; SCHEME; SPACE;
D O I：
10.1016/j.apm.2014.03.031
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
Fractional sub-diffusion equations have been widely used to model sub-diffusive systems. Most algorithms are designed for one-dimensional problems due to the memory effect in fractional derivative. In this paper, the numerical simulation of the 3D fractional sub-diffusion equation with a time fractional derivative of order alpha (0 < alpha < 1) is considered. A fractional alternating direction implicit scheme (FADIS) is proposed. We prove that FADIS is uniquely solvable, unconditionally stable and convergent in H-1 norm by the energy method. A numerical example is given to demonstrate the efficiency of FADIS. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：3695 / 3705
页数：11
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