A Second-Order Difference Scheme for Generalized Time-Fractional Diffusion Equation with Smooth Solutions-Reference-Cited by-同舟云学术

A Second-Order Difference Scheme for Generalized Time-Fractional Diffusion Equation with Smooth Solutions

Published:2023-05-23 Issue:1 Volume:24 Page:101-117
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Khibiev Aslanbek¹^ORCID,Alikhanov Anatoly¹^ORCID,Huang Chengming²

Affiliation:

1. North-Caucasus Center for Mathematical Research , North-Caucasus Federal University , Stavropol , Russia

2. School of Mathematics and Statistics , Huazhong University of Science and Technology , Wuhan , P. R. China

Abstract

Abstract In the current work, we build a difference analog of the Caputo fractional derivative with generalized memory kernel (𝜇L2-1𝜎 formula). The fundamental features of this difference operator are studied, and on its ground, some difference schemes generating approximations of the second order in time for the generalized time-fractional diffusion equation with variable coefficients are worked out. We have proved stability and convergence of the given schemes in the grid L 2

L_{2}

-norm with the rate equal to the order of the approximation error. The achieved results are supported by the numerical computations performed for some test problems.

Funder

Russian Science Foundation

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2022-0089/pdf

Reference28 articles.

1. O. P. Agrawal, Some generalized fractional calculus operators and their applications in integral equations, Fract. Calc. Appl. Anal. 15 (2012), no. 4, 700–711.

2. A. A. Alikhanov, A priori estimates for solutions of boundary value problems for equations of fractional order, Differ. Equ. 46 (2010), 660–666.