Cover Image

Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration

Time-fractional diffusion equations (TFDEs) are widely used in modeling anomalous diffusion processes, which occur in various fields such as physics, engineering, and economics. These equations offer a more accurate representation of systems where classical diffusion models fall short, particularly...

Full description

Saved in:
Bibliographic Details
Main Authors: Mohd Usran Alibubin, Jumat Sulaiman, Fatihah Anas Muhiddin, Andang Sunarto
Format: Article
Language:English
Published: e-VIBS, Faculty of Science and Natural Resources 2024
Subjects:
Q1-390 Science (General)
QC1-999 Physics
Online Access:https://eprints.ums.edu.my/id/eprint/43027/1/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/43027/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.ums.eprints.43027
record_format eprints
spelling my.ums.eprints.430272025-03-05T05:33:02Z https://eprints.ums.edu.my/id/eprint/43027/ Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration Mohd Usran Alibubin Jumat Sulaiman Fatihah Anas Muhiddin Andang Sunarto Q1-390 Science (General) QC1-999 Physics Time-fractional diffusion equations (TFDEs) are widely used in modeling anomalous diffusion processes, which occur in various fields such as physics, engineering, and economics. These equations offer a more accurate representation of systems where classical diffusion models fall short, particularly in capturing memory and hereditary properties of materials. In this paper, we employ the Caputo finite difference approximation equation for TFDEs by applying a discretization scheme based on the second-order implicit finite difference and Caputo fractional derivative operator. To solve these equations numerically, the one-dimensional TFDEs are discretized using Caputo’s implicit finite difference approximation. The corresponding system of linear approximation equations is then solved using weighted point iteration methods, specifically Successive Overrelaxation (SOR) and Gauss-Seidel (GS). Three examples are provided to evaluate the performance of these iterative methods. The numerical results demonstrate that the SOR method requires fewer iterations and reduces computational time, proving to be more efficient compared to the Gauss-Seidel method. e-VIBS, Faculty of Science and Natural Resources 2024 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/43027/1/FULL%20TEXT.pdf Mohd Usran Alibubin and Jumat Sulaiman and Fatihah Anas Muhiddin and Andang Sunarto (2024) Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration. Transactions on Science and Technology, 11 (3). pp. 165-174.
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
topic Q1-390 Science (General)
QC1-999 Physics
spellingShingle Q1-390 Science (General)
QC1-999 Physics
Mohd Usran Alibubin
Jumat Sulaiman
Fatihah Anas Muhiddin
Andang Sunarto
Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration
description Time-fractional diffusion equations (TFDEs) are widely used in modeling anomalous diffusion processes, which occur in various fields such as physics, engineering, and economics. These equations offer a more accurate representation of systems where classical diffusion models fall short, particularly in capturing memory and hereditary properties of materials. In this paper, we employ the Caputo finite difference approximation equation for TFDEs by applying a discretization scheme based on the second-order implicit finite difference and Caputo fractional derivative operator. To solve these equations numerically, the one-dimensional TFDEs are discretized using Caputo’s implicit finite difference approximation. The corresponding system of linear approximation equations is then solved using weighted point iteration methods, specifically Successive Overrelaxation (SOR) and Gauss-Seidel (GS). Three examples are provided to evaluate the performance of these iterative methods. The numerical results demonstrate that the SOR method requires fewer iterations and reduces computational time, proving to be more efficient compared to the Gauss-Seidel method.
format Article
author Mohd Usran Alibubin
Jumat Sulaiman
Fatihah Anas Muhiddin
Andang Sunarto
author_facet Mohd Usran Alibubin
Jumat Sulaiman
Fatihah Anas Muhiddin
Andang Sunarto
author_sort Mohd Usran Alibubin
title Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration
title_short Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration
title_full Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration
title_fullStr Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration
title_full_unstemmed Caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration
title_sort caputo finite difference solution for solving time-fractional diffusion equations via weighted point iteration
publisher e-VIBS, Faculty of Science and Natural Resources
publishDate 2024
url https://eprints.ums.edu.my/id/eprint/43027/1/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/43027/
_version_ 1825809977485295616
score 13.244413

Similar Items