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The Scientific World Journal
Volume 2014 (2014), Article ID 309264, 11 pages
http://dx.doi.org/10.1155/2014/309264
Research Article

Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
3Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt

Received 25 October 2013; Accepted 20 November 2013; Published 27 January 2014

Academic Editors: S. Amat, M. Inc, and S. A. Tersian

Copyright © 2014 Waleed M. Abd-Elhameed 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.

Citations to this Article [8 citations]

The following is the list of published articles that have cited the current article.

  • A. H. Bhrawy, M. A. Alghamdi, and Eman S. Alaidarous, “An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions,” Abstract and Applied Analysis, vol. 2014, pp. 1–14, 2014. View at Publisher · View at Google Scholar
  • W. M. Abd-Elhameed, “New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems,” The Scientific World Journal, vol. 2014, pp. 1–11, 2014. View at Publisher · View at Google Scholar
  • A. H. Bhrawy, “A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014. View at Publisher · View at Google Scholar
  • W. M. Abd-Elhameed, “New Galerkin operational matrix of derivatives for solving Lane-Emden singular-type equations,” European Physical Journal Plus, vol. 130, no. 3, 2015. View at Publisher · View at Google Scholar
  • F. Sacchetti, N. Colonna, R. Faccini, B. Guerard, R. Hall-Wilton, F. Murtas, C. Petrillo, A. Pietropaolo, N. Rhodes, L. Quintieri, M. Tardocchi, and P. Valente, “He-3-free neutron detectors and their applications,” European Physical Journal Plus, vol. 130, no. 3, 2015. View at Publisher · View at Google Scholar
  • W. M. Abd-Elhameed, “Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials,” Abstract and Applied Analysis, vol. 2015, pp. 1–10, 2015. View at Publisher · View at Google Scholar
  • W. M. Abd-Elhameed, E. H. Doha, Y. H. Youssri, and M. A. Bassuony, “New Tchebyshev-Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations,” Numerical Methods for Partial Differential Equations, 2016. View at Publisher · View at Google Scholar
  • W. M. Abd-Elhameed, and Y. H. Youssri, “Spectral Solutions for Fifth-Order Boundary Value Problems Using Generalized Jacobi Operational Matrix of Derivatives,” International Journal of Applied and Computational Mathematics, 2017. View at Publisher · View at Google Scholar