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...
| Published in: | Journal of Advanced Research in Applied Sciences and Engineering Technology |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Semarak Ilmu Publishing
2025
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| 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 |
| Summary: | 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. |
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| ISSN: | 24621943 |
| DOI: | 10.37934/araset.48.1.168179 |