Preconditioned Gauss-Seidel Method for the Solution of Time-fractional Diffusion Equations

A. Sunarto, J. Sulaiman

2019

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

Paper Citation

in Harvard Style

Sunarto A. and Sulaiman J. (2019). 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 - Volume 1: ICASESS, ISBN 978-989-758-452-7, pages 268-273. DOI: 10.5220/0009882502680273

in Bibtex Style

@conference{icasess19,
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 - Volume 1: ICASESS,},
year={2019},
pages={268-273},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0009882502680273},
isbn={978-989-758-452-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Applied Science, Engineering and Social Sciences - Volume 1: 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 - 2019
SP - 268
EP - 273
DO - 10.5220/0009882502680273