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

页码：3695 / 3705

页数：11

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