A SOR solution of one-dimensional telegraph equations by using newly established Redlich-Kister finite difference schemes

Mohd Norfadli Suardi and Jumat Sulaiman (2021) A SOR solution of one-dimensional telegraph equations by using newly established Redlich-Kister finite difference schemes.

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Official URL: https://oer.ums.edu.my/handle/oer_source_files/187...

Abstract

Various finite difference schemes have been established to discretize boundary value problems. Therefore, this paper proposes a numerical solution based on newly established second-order Redlich-Kister Finite Difference (RKFD) discretization schemes to approximate the one-dimensional second-order linear hyperbolic telegraph equation. By doing the discretisation process, the RKFD approximation equation leads to a large-scale and sparse system of RKFD approximation equations, which can be solved iteratively using the Gauss-Seidel (GS) Successive Over-Relaxation (SOR) iterative methods. In order to validate the capability of the SOR iterative method, two model examples have been solved iteratively via the SOR iteration and then compared to the GS iterative method at five different mesh sizes. The comparison results for both iterative methods are illustrated by focusing on three measuring parameters: number of iterations, execution time, and maximum norm. As can be observed from the numerical results, the proposed method approximates the exact solution very well.

Item Type:	Proceedings
Keyword:	SOR iteration, Redlich-Kister finite difference, Finite difference, HyperbolicB Telegraph problem
Subjects:	H Social Sciences > HE Transportation and Communications > HE1-9990 Transportation and communications > HE7601-8700.9 Telecommunication industry. Telegraph > HE8660-8688 Wireless telegraph. Radiotelegraphy Q Science > Q Science (General) > Q1-390 Science (General)
Department:	FACULTY > Faculty of Science and Natural Resources
Depositing User:	SITI AZIZAH BINTI IDRIS -
Date Deposited:	25 Oct 2024 09:28
Last Modified:	25 Oct 2024 09:28
URI:	https://eprints.ums.edu.my/id/eprint/41614

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