**Commenced**in January 2007

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**Edition:**International

**Paper Count:**31742

##### MEGSOR Iterative Scheme for the Solution of 2D Elliptic PDE's

**Authors:**
J. Sulaiman,
M. Othman,
M. K. Hasan

**Abstract:**

Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

**Keywords:**
MEG iteration,
second-order finite difference,
weighted parameter.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1334564

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