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Dr. Shaaban Abd El-Gaid Meligy Mahmoud :: Publications:

Relaxation Parameters and Composite Refinement Techniques
Authors: Sh. A. Meligy; I. K. Youssef
Year: 2022
Keywords: Not Available
Journal: Results in Applied Mathematics
Volume: 15
Issue: Not Available
Pages: Article 100282
Publisher: Elsevier BV
Local/International: International
Paper Link:
Full paper Shaaban Abd El-Gaid Meligy Mahmoud_Relaxation Parameters and CompositeRefinementTechniques.pdf
Supplementary materials Not Available

A composite refinement technique for two stationary iterative methods, one of them contains a relaxation parameter, is introduced. Four new techniques, Jacobi successive over relaxation (SOR) composite refinement (RJSOR), SOR Jacobi composite refinement (RSORJ), Gauss–Seidel (GS) SOR composite refinement (RGSSOR) and SOR with GS composite refinement (RSORGS) are compared with their classical forms. The efficient performance of the new forms is well established and confirmed through numerical example. The computational costs and the speed of convergence are considered. The decrease in the required number of iteration is established through the calculation of the spectral radius of the iteration matrices. It is illustrated that the convergence of Jacobi and Gauss–Seidel methods engage the divergence and extend the domain of convergence in the SOR method in the refinement technique. The calculations and graphs are performed by computer algebra system, Mathematica.

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