Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript

Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript

This study presents numerical solution of time-fractional linear parabolic partial differential equations (PDEs) using the Caputo finite difference scheme. The discretization process is based on the second-order implicit finite difference scheme and the Caputo fractional derivative operator. The res...

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Bibliographic Details
Published in:Journal of Advanced Research in Applied Sciences and Engineering Technology
Main Author: Alibubin M.U.; Sulaiman J.; Muhiddin F.A.; Sunarto A.
Format: Article
Language:English
Published: Semarak Ilmu Publishing 2025
Online Access:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85199860902&doi=10.37934%2faraset.48.1.168179&partnerID=40&md5=2cd576bfad3313dd6ecc74ef5dfafe5f
id 2-s2.0-85199860902
spelling 2-s2.0-85199860902
Alibubin M.U.; Sulaiman J.; Muhiddin F.A.; Sunarto A.
Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript
2025
Journal of Advanced Research in Applied Sciences and Engineering Technology
48
1
10.37934/araset.48.1.168179
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85199860902&doi=10.37934%2faraset.48.1.168179&partnerID=40&md5=2cd576bfad3313dd6ecc74ef5dfafe5f
This study presents numerical solution of time-fractional linear parabolic partial differential equations (PDEs) using the Caputo finite difference scheme. The discretization process is based on the second-order implicit finite difference scheme and the Caputo fractional derivative operator. The resulting system of linear approximation equations is solved using the Kaudd Successive Over Relaxation (KSOR) iterative method. A comparison is made with the Gauss-Seidel (GS) iterative method through three numerical examples. The results demonstrate that the KSOR method requires fewer iterations and reduced computational time compared to the GS method. © 2025, Semarak Ilmu Publishing. All rights reserved.
Semarak Ilmu Publishing
24621943
English
Article
author Alibubin M.U.; Sulaiman J.; Muhiddin F.A.; Sunarto A.
spellingShingle Alibubin M.U.; Sulaiman J.; Muhiddin F.A.; Sunarto A.
Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript
author_facet Alibubin M.U.; Sulaiman J.; Muhiddin F.A.; Sunarto A.
author_sort Alibubin M.U.; Sulaiman J.; Muhiddin F.A.; Sunarto A.
title Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript
title_short Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript
title_full Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript
title_fullStr Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript
title_full_unstemmed Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript
title_sort Implementation of the KSOR Method for Solving One-Dimensional Time-Fractional Parabolic Partial Differential Equations with the Caputo Finite Difference Scheme Title of Manuscript
publishDate 2025
container_title Journal of Advanced Research in Applied Sciences and Engineering Technology
container_volume 48
container_issue 1
doi_str_mv 10.37934/araset.48.1.168179
url https://www.scopus.com/inward/record.uri?eid=2-s2.0-85199860902&doi=10.37934%2faraset.48.1.168179&partnerID=40&md5=2cd576bfad3313dd6ecc74ef5dfafe5f
description This study presents numerical solution of time-fractional linear parabolic partial differential equations (PDEs) using the Caputo finite difference scheme. The discretization process is based on the second-order implicit finite difference scheme and the Caputo fractional derivative operator. The resulting system of linear approximation equations is solved using the Kaudd Successive Over Relaxation (KSOR) iterative method. A comparison is made with the Gauss-Seidel (GS) iterative method through three numerical examples. The results demonstrate that the KSOR method requires fewer iterations and reduced computational time compared to the GS method. © 2025, Semarak Ilmu Publishing. All rights reserved.
publisher Semarak Ilmu Publishing
issn 24621943
language English
format Article
accesstype
record_format scopus
collection Scopus
_version_ 1809678469685051392

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