Volume 10, Issue 1 (4-2024)                   mmr 2024, 10(1): 51-69 | Back to browse issues page

XML Persian Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Kheirkhah F, Hajipour M. An accurate numerical method for solving the variable-order fractional diffusion problem. mmr 2024; 10 (1) :51-69
URL: http://mmr.khu.ac.ir/article-1-3303-en.html
1- Sahand University of Technology
2- Sahand University of Technology , hajipour@sut.ac.ir
Abstract:   (584 Views)
In this paper, a high-order numerical method is designed and implemented to solve a boundary value problem governed by the variable-order fractional diffusion equation. This equation contains a variable-order fractional time-derivative and a second-order spatial-derivative. To develop this novel method, a compact finite difference formula and a weighted shifted Grunwald-Letnikov operator are used for spatial and temporal discretization, respectively. It is shown that this method is of fourth- and second-order of convergence accuracy in spatial and time directions, respectively. Also, the solvability, stability and convergence of the peresent method are investigated. To verify the efficiency and high accuracy of this method, some numerical examples and comparative results are presented.
Full-Text [PDF 460 kb]   (236 Downloads)    
Type of Study: Research Paper | Subject: Mat
Received: 2022/11/20 | Revised: 2024/07/10 | Accepted: 2023/10/9 | Published: 2024/04/27 | ePublished: 2024/04/27

Add your comments about this article : Your username or Email:
CAPTCHA

Send email to the article author


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2024 CC BY-NC 4.0 | Mathematical Researches

Designed & Developed by : Yektaweb