Implementation of the 4EGKSOR for Solving One-Dimensional Time-Fractional Parabolic Equations with Grünwald Implicit Difference Scheme

• Main Authors: Fatihah Anas Muhiddin, Jumat Sulaiman, Andang Sunarto
• Format: Conference or Workshop Item
• Language: English
• Published: Springer Link 2020
• Subjects: QA Mathematics
• Online Access: https://eprints.ums.edu.my/id/eprint/25317/1/Implementation%20of%20the%204EGKSOR%20for%20Solving%20One-Dimensional%20Time-Fractional%20Parabolic%20Equations%20with%20Gr%C3%83%C2%BCnwald%20Implicit%20Difference%20Scheme.pdf; https://eprints.ums.edu.my/id/eprint/25317/; https://doi.org/10.1007/978-981-15-0058-9_4

Solving one-dimensional time-fractional parabolic equations using numerical technique will require some iterative solver to solve the generated large and sparse linear systems. Thus, by considering the advantages of the Explicit Group iteration technique together with the Kaudd SOR (KSOR) iterative method, this paper examines the efficiency of the four-point Explicit Group Kaudd SOR (4EGKSOR) iterative method to solve the approximation equations generated from discretization of one-dimensional time-fractional parabolic equations using the finite difference scheme with the second order Grünwald Implicit difference scheme. In addition, the formulation and implementation of the proposed method to solve the problem are also presented. Numerical result and comparison with four-point Explicit Group Gauss-Seidel (4EGGS) method are given to illustrate the efficiency of the proposed method.