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Authors: A. Sunarto 1 and J. Sulaiman 2

Affiliations: 1 Department Tadris Matematika, IAIN Bengkulu, Indonesia ; 2 Department Matemathics with economics, Universiti Malaysia Sabah, Indonesia

Keyword(s): Linear System, Preconditioned Gauss-Seidel (PGS) method

Abstract: In this paper, we deal with the application of an unconditionally implicit finite difference approximation equation of the one-dimensional linear time fractional diffusion equations via the Caputo’s time fractional derivative. Based on this implicit approximation equation, the corresponding linear system can be generated in which its coefficient matrix is large scale and sparse. To speed up the convergence rate in solving the linear system iteratively, we construct the corresponding preconditioned linear system. Then we formulate and implement the Preconditioned Gauss-Seidel (PGS) iterative method for solving the generated linear system. One example of the problem is presented to illustrate the effectiveness of PGS method. The numerical results of this study show that the proposed iterative method is superior to the basic GS iterative method

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Paper citation in several formats:
Sunarto, A. and Sulaiman, J. (2020). Preconditioned Gauss-Seidel Method for the Solution of Time-fractional Diffusion Equations. In Proceedings of the 2nd International Conference on Applied Science, Engineering and Social Sciences - ICASESS; ISBN 978-989-758-452-7, SciTePress, pages 268-273. DOI: 10.5220/0009882502680273

@conference{icasess20,
author={A. Sunarto. and J. Sulaiman.},
title={Preconditioned Gauss-Seidel Method for the Solution of Time-fractional Diffusion Equations},
booktitle={Proceedings of the 2nd International Conference on Applied Science, Engineering and Social Sciences - ICASESS},
year={2020},
pages={268-273},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0009882502680273},
isbn={978-989-758-452-7},
}

TY - CONF

JO - Proceedings of the 2nd International Conference on Applied Science, Engineering and Social Sciences - ICASESS
TI - Preconditioned Gauss-Seidel Method for the Solution of Time-fractional Diffusion Equations
SN - 978-989-758-452-7
AU - Sunarto, A.
AU - Sulaiman, J.
PY - 2020
SP - 268
EP - 273
DO - 10.5220/0009882502680273
PB - SciTePress