Implementation of the ksor method for solving one-dimensional time-fractional parabolic partial differential equations with the caputo finite difference scheme title of manuscript

• Main Authors: Mohd Usran Alibubin, Jumat Sulaiman, Fatihah Anas Muhiddin, Andang Sunarto
• Format: Article
• Language: English; English
• Published: Penerbit Akademia Baru 2025
• Subjects: QA1-939 Mathematics; QA299.6-433 Analysis
• Online Access: https://eprints.ums.edu.my/id/eprint/41923/1/ABSTRACT.pdf; https://eprints.ums.edu.my/id/eprint/41923/2/FULL%20TEXT.pdf; https://eprints.ums.edu.my/id/eprint/41923/; https://doi.org/10.37934/araset.48.1.168179
• Institution: Universiti Malaysia Sabah

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.