A high-order L2 type difference scheme for the time-fractional diffusion equation

被引：32

作者：

Alikhanov, Anatoly A. ^{[1
]}

Huang, Chengming ^{[2
]}

机构：

[1] North Caucasus Fed Univ, North Caucasus Ctr Math Res, Pushkin Str 1, Stavropol 355017, Russia

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2021年 / 411卷

关键词：

Fractional diffusion equation; Finite difference method; Stability; Convergence; BOUNDARY-VALUE-PROBLEMS; VARIABLE-ORDER; APPROXIMATIONS;

D O I：

10.1016/j.amc.2021.126545

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present paper is devoted to constructing L2 type difference analog of the Caputo fractional derivative. The fundamental features of this difference operator are studied and it is used to construct difference schemes generating approximations of the second and fourth order in space and the (3 - alpha)th-order in time for the time fractional diffusion equation with variable coefficients. Difference schemes were also constructed for the variable-order diffusion equation and the generalized fractional-order diffusion equation of the Sobolev type. Stability of the schemes under consideration as well as their convergence with the rate equal to the order of the approximation error are proven. The received results are supported by the numerical computations performed for some test problems. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：19

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