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Abstract and Applied Analysis
Volume 2014, Article ID 796286, 7 pages
Research Article

On Bernstein Polynomials Method to the System of Abel Integral Equations

1Department of Mathematics, Islamic Azad University, Urmia Branch, P.O. BOX 969, Urmia, Iran
2Department of Physics, Islamic Azad University, Urmia Branch, P.O. BOX 969, Urmia, Iran
3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
4Department of Mathematics and Computer Science, Çankaya University, 06530 Ankara, Turkey
5Institute of Space Sciences, P.O. Box MG-23, 76900 Magurele-Bucharest, Romania

Received 20 November 2013; Revised 3 March 2014; Accepted 4 March 2014; Published 7 May 2014

Academic Editor: Hossein Jafari

Copyright © 2014 A. Jafarian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. For this aim, first the truncated Bernstein series polynomials of the solution functions are substituted in the given problem. Using some properties of these polynomials, the solution of the problem is reduced to solve a linear system of algebraic equations. In order to confirm the reliability and accuracy of the proposed method, some weakly Abel integral equations systems with comparisons are solved in detail as numerical examples.