Abstract and Applied Analysis

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

A. H. Bhrawy, M. A. Alghamdi, and D. Baleanu

Full-text: Open access

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

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 513808, 9 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450256

Digital Object Identifier
doi:10.1155/2013/513808

Mathematical Reviews number (MathSciNet)
MR3121407

Zentralblatt MATH identifier
1291.65243

Citation

Bhrawy, A. H.; Alghamdi, M. A.; Baleanu, D. Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 513808, 9 pages. doi:10.1155/2013/513808. https://projecteuclid.org/euclid.aaa/1393450256


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