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Abstract and Applied Analysis
Volume 2014, Article ID 623763, 8 pages
Research Article

Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

1Faculty of Basic Science, Babol University of Technology, P.O. Box 47148-71167, Babol, Iran
2Department of Mathematics, Cankaya University, Ogretmenler Caddesi 14, Balgat, 06530 Ankara, Turkey
3Institute of Space Sciences, P.O. Box MG 23, Magurele, 077125 Bucharest, Romania
4Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia

Received 22 November 2013; Accepted 9 January 2014; Published 23 February 2014

Academic Editor: Carlo Cattani

Copyright © 2014 Mohsen Alipour 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.


We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.