AN APPLICATION OF FINITE DIFFERENCE METHOD TO SOLVE ELLIPTIC PDE'S WITH USE OF GS AND SOR ITERATIVE METHODS

Authors

  • Omar Ali Aleyan Mathematics Department, Science Faculty, AL-Asmarya Islamic University, Zliten, Libya

DOI:

https://doi.org/10.59743/

Keywords:

Poisson's Equation, Laplace's Equation, Approximation solution, finite difference method (FDM), GS and SOR methods

Abstract

1.1.1    In this paper finding an approximation solution of a linear system  By the Gauss Seidel (GS) and the Successive Over-Relaxation (SOR) iterative methods, this system was derived from an elliptic partial differential equation by adopting the finite difference method. These methods are applied to two different examples. The results showed that the convergent to the approximate solution of them with special choice of  the parameter  for the SOR iterative method and compared the results.

Downloads

Download data is not yet available.

References

Aleyan O. A.: Applications of Finite Element Method to Solve Elliptic Partial Differential Equations Using Iterative Methods. An Academic, Intellectual, Cultural, Comprehensive and Arbitrated Journal Issued by the Faculty of Arts and Sciences in Zliten, Al-Mergeb. Issue No.21 2012 AS –SAYIF (December) .

Aleyan O. A.: On matrix splitting and application into iterative methods for linear systems An Academic, Intellectual, Cultural, Comprehensive and Arbitrated Journal Issued by the Faculty of Arts and Sciences in Zliten, Al-Merqab. Issue No. 18 2009 AS –SAYIF (JUNE) 1377.

R. J. Leveque Finite Difference Method for Ordinary and Partial Differential Equations, SIAM, 2007.

Ortega, J.M. and Rheinboldt, W.C. Iterative solution of linear systems, Plenum Press, New York, 1988.

Horn, R.A. and Johnson, C.R. Matrix analysis, Cambridge University Press, Cambridge, 1986.

Miroslav Fiedler., Special matrices and their applications in numerical mathematics, Kluwer, 1986.

Richard L. Burden and J. Donglas Faires. Numerical analysis, third edition prindle, Weber & Schmidt, Boston, 1985.

Berman, A. and Plemmons, R. Nonnegative matrices in the mathematical sciences, Academic Press, New York, 1979.

Young, D. Iterative solution of large linear systems, Academic Press, New York, 1977.

I. N. Sneddom Numerical Solution of Partial Differential Equation McGrow-Hill Co, New York, 1975.

Downloads

Published

31-07-2020

Issue

Vol. 4 No. 2 (2020)

Section

المقالات

Categories

License

Copyright (c) 2020 Journal of the Academic Forum

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Aleyan, O. A. (2020). AN APPLICATION OF FINITE DIFFERENCE METHOD TO SOLVE ELLIPTIC PDE’S WITH USE OF GS AND SOR ITERATIVE METHODS . Journal of the Academic Forum, 4(2), 379-394. https://doi.org/10.59743/