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

Abstract and Applied Analysis

Research Article

D. Baleanu¹  M. A. Alghamdi³  A. H. Bhrawy² 

[1] Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia, kau.edu.sa;Department of Mathematics and Computer Sciences, Cankaya University, Eskisehir Yolu 29.km, 06810 Ankara, Turkey, cankaya.edu.tr;Institute of Space Sciences, P.O. Box MG-23, 76900 Magurele-Bucharest, Romania, spacescience.ro;Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia, kau.edu.sa;Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt, bsu.edu.eg;Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia, kau.edu.sa

Others  :  1297045
DOI  :  10.1155/2013/513808

 received in 2013-08-24, accepted in 2013-09-18,  发布年份 2013

【 摘 要 】

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 θ-method, continuous Runge-Kutta method, and reproducing kernel Hilbert space method.

【 授权许可】

CC BY   
Copyright © 2013 A. H. Bhrawy et al. 2013

【 图 表 】

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