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Advances in Numerical Analysis
Volume 2012 (2012), Article ID 868279, 14 pages
Research Article

Solution of Nonlinear Volterra-Fredholm Integrodifferential Equations via Hybrid of Block-Pulse Functions and Lagrange Interpolating Polynomials

Department of Mathematical Sciences, Isfahan University of Technology, P.O. Box 8415683111, Isfahan, Iran

Received 22 May 2012; Accepted 8 November 2012

Academic Editor: Alfredo Bermudez De Castro

Copyright © 2012 Hamid Reza Marzban and Sayyed Mohammad Hoseini. 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.


An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations to the solution of algebraic equations whose solution is much more easier than the original one. The validity and applicability of the proposed method are demonstrated through illustrative examples. The method is simple, easy to implement and yields very accurate results.