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

页码：12 / 22

页数：11

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