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Abstract and Applied Analysis
Volume 2011, Article ID 947230, 21 pages
Research Article

A Jacobi Dual-Petrov-Galerkin Method for Solving Some Odd-Order Ordinary Differential Equations

1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt
4Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo 11931, Egypt

Received 31 October 2010; Revised 13 February 2011; Accepted 16 February 2011

Academic Editor: Simeon Reich

Copyright © 2011 E. H. Doha 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 Jacobi dual-Petrov-Galerkin (JDPG) method is introduced and used for solving fully integrated reformulations of third- and fifth-order ordinary differential equations (ODEs) with constant coefficients. The reformulated equation for the 𝐽 th order ODE involves 𝑛 -fold indefinite integrals for 𝑛 = 1 , … , 𝐽 . Extension of the JDPG for ODEs with polynomial coefficients is treated using the Jacobi-Gauss-Lobatto quadrature. Numerical results with comparisons are given to confirm the reliability of the proposed method for some constant and polynomial coefficients ODEs.