Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation

被引：66
作者：
Alikhanov, Anatoly A. [1 ]
机构：
[1] Russian Acad Sci, Res Inst Appl Math & Automat, Ul Shortanova 89 A, Nalchik 360000, Russia
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 268卷
基金：
俄罗斯基础研究基金会;
关键词：
Fractional order diffusion equation; Fractional derivative; A priori estimate; Difference scheme; Stability and convergence; FRACTIONAL-ORDER; CONVERGENCE; STABILITY; SCHEMES;
D O I：
10.1016/j.amc.2015.06.045
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using the method of the energy inequalities. The stability and convergence of the difference schemes follow from a priory estimates. The credibility of the obtained results is verified by performing numerical calculations for test problems. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：12 / 22
页数：11
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