Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian

被引：16

作者：

Fardi, M. ^{[1
]}

Zaky, M. A. ^{[2
]}

Hendy, A. S. ^{[3
,4
]}

机构：

[1] Shahrekord Univ, Fac Math Sci, Dept Appl Math, POB 115, Shahrekord, Iran

[2] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh, Saudi Arabia

[3] Ural Fed Univ, Inst Nat Sci & Math, Dept Computat Math & Comp Sci, 19 Mira St, Ekaterinburg 620002, Russia

[4] Benha Univ, Fac Sci, Dept Math, Banha 13511, Egypt

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2023年 / 206卷

关键词：

Multi-term fractional derivative; Distributed fractional derivative; Fractional Laplacian; Non-uniform mesh; Convergence and stability estimates; NUMERICAL APPROXIMATION; CONVOLUTION QUADRATURE; DIFFUSION-EQUATIONS; ERROR ESTIMATE;

D O I：

10.1016/j.matcom.2022.12.009

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, the multi-term temporal fractional order and temporal distributed-order parabolic equations with fractional Laplacian are numerically investigated. Several unconditional stable difference schemes based on non-uniform meshes for solving these differential equations are provided. We find that the constructed nonuniform difference schemes are convergent and it has been shown that the temporal convergence rate is faster and more accurate compared to the uniform difference schemes in case of nonsmooth solutions with respect to time. Some numerical examples are given to verify the theoretical findings. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：614 / 635

页数：22