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Mathematical Problems in Engineering
Volume 2013, Article ID 760515, 5 pages
Research Article

Solving Hammerstein Type Integral Equation by New Discrete Adomian Decomposition Methods

1Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt

Received 2 May 2013; Accepted 4 October 2013

Academic Editor: Metin O. Kaya

Copyright © 2013 Huda O. Bakodah and Mohamed Abdalla Darwish. 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.


New discrete Adomian decomposition methods are presented by using some identified Clenshaw-Curtis quadrature rules. We investigate two mixed quadrature rules one of precision five and the other of precision seven. The first rule is formed by using the Fejér second rule of precision three and Simpson rule of precision three, while the second rule is formed by using the Fejér second rule of precision five and the Boole rule of precision five. Our methods were applied to a nonlinear integral equation of the Hammerstein type and some examples are given to illustrate the validity of our methods.