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Mathematical Problems in Engineering
Volume 2013, Article ID 434753, 7 pages
Research Article

Numerical and Analytical Study for Fourth-Order Integro-Differential Equations Using a Pseudospectral Method

1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
2Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt
3Department of Mathematics, Faculty of Science, Mansoura University, Damietta 35516, Egypt

Received 16 July 2012; Accepted 2 December 2012

Academic Editor: Pedro Ribeiro

Copyright © 2013 N. H. Sweilam 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.


A numerical method for solving fourth-order integro-differential equations is presented. This method is based on replacement of the unknown function by a truncated series of well-known shifted Chebyshev expansion of functions. An approximate formula of the integer derivative is introduced. The introduced method converts the proposed equation by means of collocation points to system of algebraic equations with shifted Chebyshev coefficients. Thus, by solving this system of equations, the shifted Chebyshev coefficients are obtained. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. Numerical results are performed in order to illustrate the usefulness and show the efficiency and the accuracy of the present work.