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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 513808, 9 pages
http://dx.doi.org/10.1155/2013/513808
Research Article

Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt
3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4Department of Mathematics and Computer Sciences, Cankaya University, Eskisehir Yolu 29.km, 06810 Ankara, Turkey
5Institute of Space Sciences, P.O. Box MG-23, 76900 Magurele-Bucharest, Romania

Received 24 August 2013; Accepted 18 September 2013

Academic Editor: Soheil Salahshour

Copyright © 2013 A. H. Bhrawy 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.

Abstract

The shifted Jacobi-Gauss-Lobatto pseudospectral (SJGLP) method is applied to neutral functional-differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss-Lobatto quadrature. The shifted Legendre-Gauss-Lobatto Pseudo-spectral and Chebyshev-Gauss-Lobatto Pseudo-spectral methods can be obtained as special cases of the underlying method. Moreover, the SJGLP method is extended to numerically approximate the nonlinear high-order NFDE with proportional delay. Some examples are displayed for implicit and explicit forms of NFDEs to demonstrate the computation accuracy of the proposed method. We also compare the performance of the method with variational iteration method, one-leg -method, continuous Runge-Kutta method, and reproducing kernel Hilbert space method.