Boundary Value Problems on Triangular Domains and MKSOR Methods
Applied and Computational Mathematics
Volume 3, Issue 3, June 2014, Pages: 90-99
Received: May 29, 2014; Accepted: Jun. 16, 2014; Published: Jun. 30, 2014
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Authors
I. K. Youssef, Dept. of Mathematics, Faculty of Science, Ain Shams Univeristy, Abbassia, 11566, Cairo, Egypt
Sh. A. Meligy, Dept. of Engineering Mathematics and Physics, Faculty of Engineering Shoubra, Benha Univeristy, Cairo, Egypt
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Abstract
The performance of six variants of the successive overrelaxation methods (SOR) are considered for an algebraic system arising from a finite difference treatment of an elliptic equation of Partial Differential Equations (PDEs) on a triangular region. The consistency of the finite difference representation of the system is achieved. In the finite difference method one obtains an algebraic system corresponding to the boundary value problem (BVP). The block structure of the algebraic system corresponding to four different labeling (the natural, the red- black and green (RBG), the electronic and the spiral) of the grid points is considered. Also, algebraic systems obtained from BVP with mixed derivatives are well established. Determination of the optimal relaxation parameters on the bases of the graphical representation of the spectral radius of the iteration matrices for the SOR, the Modified Successive over relaxation (MSOR) and their new variants KSOR, MKSOR, MKSOR1 and MKSOR2 are considered. Application of the treatment to two numerical examples is considered.
Keywords
SOR, KSOR, MKSOR, MKSOR1, Triangular Grid and Grid Labeling
To cite this article
I. K. Youssef, Sh. A. Meligy, Boundary Value Problems on Triangular Domains and MKSOR Methods, Applied and Computational Mathematics. Vol. 3, No. 3, 2014, pp. 90-99. doi: 10.11648/j.acm.20140303.14
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