Two Alternating Direction Implicit Difference Schemes for Two-Dimensional Distributed-Order Fractional Diffusion Equations

被引：58

作者：

Gao, Guang-hua ^{[1
]}

Sun, Zhi-zhong ^{[2
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210023, Jiangsu, Peoples R China

[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2016年 / 66卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Distributed-order fractional diffusion equations; High-order approximation; Fractional derivative; Difference scheme; ADI; Stability; Convergence; ANOMALOUS SUBDIFFUSION EQUATION; BOUNDARY-VALUE-PROBLEMS; NUMERICAL-METHODS; SUB-DIFFUSION; APPROXIMATIONS; ADI;

D O I：

10.1007/s10915-015-0064-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two alternating direction implicit difference schemes are derived for two-dimensional distributed-order fractional diffusion equations. It is proved that the schemes are unconditionally stable and convergent in a discrete norm with the convergence orders and respectively, where and are the step sizes in time, space and distributed order. Several numerical examples are given to confirm the theoretical results.

引用

页码：1281 / 1312

页数：32

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