A compact finite difference scheme for the fractional sub-diffusion equations

被引：352
|
作者：
Gao, Guang-hua [1 ]
Sun, Zhi-zhong [1 ]
机构：
[1] Southeast Univ, Dept Math, Nanjing 211189, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2011年 / 230卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Fractional sub-diffusion equation; L1; discretization; Compact scheme; Stability; Convergence; Energy method; ANOMALOUS SUBDIFFUSION EQUATION; IMPLICIT NUMERICAL-METHOD; STABILITY; APPROXIMATIONS; DISPERSION; ACCURACY; ORDER;
D O I：
10.1016/j.jcp.2010.10.007
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, a compact finite difference scheme for the fractional sub-diffusion equations is derived. After a transformation of the original problem, the L1 discretization is applied for the time-fractional part and fourth-order accuracy compact approximation for the second-order space derivative. The unique solvability of the difference solution is discussed. The stability and convergence of the finite difference scheme in maximum norm are proved using the energy method, where a new inner product is introduced for the theoretical analysis. The technique is quite novel and different from previous analytical methods. Finally, a numerical example is provided to show the effectiveness and accuracy of the method. (C) 2010 Elsevier Inc. All rights reserved.
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页码：586 / 595
页数：10
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