Computational Approach via HalfSweep Similarity and SOR Schemes for 2D Hyperbolic Telegraph Equations
International Journal of Engineering Trends and Technology (IJETT)  

© 2022 by IJETT Journal  
Volume70 Issue9 

Year of Publication : 2022  
Authors : Nur Afza Mat Ali, Jumat Sulaiman, Azali Saudi, Nor Syahida Mohamad 

DOI : 10.14445/22315381/IJETTV70I9P205 
How to Cite?
Nur Afza Mat Ali, Jumat Sulaiman, Azali Saudi, Nor Syahida Mohamad, "Computational Approach via HalfSweep Similarity and SOR Schemes for 2D Hyperbolic Telegraph Equations ," International Journal of Engineering Trends and Technology, vol. 70, no. 9, pp. 4756, 2022. Crossref, https://doi.org/10.14445/22315381/IJETTV70I9P205
Abstract
This paper uses the similarity transformation to get similar solutions to the twodimensional hyperbolic telegraph equation (2D HTE). The similarity solution of 2D HTE is then derived using a rotated fivepoint similarity finite difference (SFD) discretization scheme to obtain the rotated fivepoint SFD approximation equation. Gathering rotated approximation equations generate a linear system with largescale and sparse matrix characteristics. Since then, the linear system has been solved using the halfsweep similarity technique via halfsweep successive overrelaxation (HSSORSFD) iteration. Three numerical examples are presented in this paper to validate the performance of the HSSORSFD iteration in solving 2D HTE. The numerical findings showed that the version of HSSORSFD iteration is the best compared to the standard similarity methods: fullsweep GaussSeidel (FSGSSFD) and fullsweep SOR (FSSORSFD) iterations in terms of iteration number and computational time.
Keywords
Twodimensional hyperbolic telegraph equation, Similarity transformation, Similarity solution, Rotated similarity finite difference method, Similarity halfsweep SOR method.
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