Some high-order difference schemes for the distributed-order differential equations

被引：82
|
作者：
Gao, Guang-hua [1 ]
Sun, Hai-wei [2 ]
Sun, Zhi-zhong [3 ]
机构：
[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210023, Jiangsu, Peoples R China
[2] Univ Macau, Dept Math, Macau, Peoples R China
[3] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2015年 / 298卷
基金：
中国国家自然科学基金;
关键词：
Distributed-order differential equations; High-order approximation; Fractional derivative; Difference scheme; Stability; Convergence; FRACTIONAL DIFFUSION EQUATION; ANOMALOUS SUBDIFFUSION EQUATION; NEUMANN BOUNDARY-CONDITIONS; HIGH SPATIAL ACCURACY; SUB-DIFFUSION; WAVE EQUATION; NUMERICAL-SOLUTION; APPROXIMATIONS; STABILITY; SYSTEM;
D O I：
10.1016/j.jcp.2015.05.047
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
Two difference schemes are derived for both one-dimensional and two-dimensional distributed-order differential equations. It is proved that the schemes are unconditionally stable and convergent in an L-1(L-infinity) norm with the convergence orders O(tau(2)+ h(2)+ Delta alpha(2)) and O(tau(2)+ h(4)+ Delta alpha(4)) , respectively, where tau, h and Delta alpha are the step sizes in time, space and distributed-order variables. Several numerical examples are given to confirm the theoretical results. (C) 2015 Elsevier Inc. All rights reserved.
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页码：337 / 359
页数：23
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