Numerical method for two dimensional fractional reaction subdiffusion equation

被引：12
作者：
Huang, H. [1 ]
Cao, X. [1 ]
机构：
[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
来源：
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS | 2013年 / 222卷 / 08期
基金：
中国国家自然科学基金;
关键词：
FINITE-DIFFERENCE APPROXIMATIONS; DIFFUSION EQUATION; STABILITY;
D O I：
10.1140/epjst/e2013-01977-9
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, a new numerical algorithm for solving two dimensional fractional reaction subdiffusion equation is proposed. The stability and convergency of this method are investigated by the Fourier analysis. Theoretical analysis and numerical experiment demonstrate that the proposed method is effective for solving the two dimensional fractional reaction subdiffusion equation.
引用
收藏
页码：1961 / 1973
页数：13
相关论文
共 26 条
[1]  
[Anonymous], 2000, Applications of Fractional Calculus in Physics
[2]  
[Anonymous], 1999, FRACTIONAL DIFFERENT
[3]   Numerical Method for the Time Fractional Fokker-Planck Equation [J].
Cao, Xue-Nian ;
Fu, Jiang-Li ;
Huang, Hu .
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2012, 4 (06) :848-863
[4]   Finite difference methods and a fourier analysis for the fractional reaction-subdiffusion equation [J].
Chen, Chang-ming ;
Liu, F. ;
Burrage, K. .
APPLIED MATHEMATICS AND COMPUTATION, 2008, 198 (02) :754-769
[5]   A Fourier method for the fractional diffusion equation describing sub-diffusion [J].
Chen, Chang-Ming ;
Liu, F. ;
Turner, I. ;
Anh, V. .
JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 227 (02) :886-897
[6]  
Chen CM, 2012, MATH COMPUT, V81, P345, DOI 10.1090/S0025-5718-2011-02447-6
[7]   Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation [J].
Chen, Chang-Ming ;
Liu, Fawang ;
Turner, Ian ;
Anh, Vo .
NUMERICAL ALGORITHMS, 2010, 54 (01) :1-21
[8]   Detailed error analysis for a fractional Adams method [J].
Diethelm, K ;
Ford, NJ ;
Freed, AD .
NUMERICAL ALGORITHMS, 2004, 36 (01) :31-52
[9]   Algorithms for the fractional calculus: A selection of numerical methods [J].
Diethelm, K ;
Ford, NJ ;
Freed, AD ;
Luchko, Y .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2005, 194 (6-8) :743-773
[10]   Mixed spline function method for reaction-subdiffusion equations [J].
Ding, Hengfei ;
Li, Changpin .
JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 242 :103-123
123