Abstract and Applied Analysis
Volume 2013 (2013), Article ID 198926, 11 pages
http://dx.doi.org/10.1155/2013/198926
Research Article

Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications

F. Toutounian,1,2 Emran Tohidi,1 and A. Kilicman3

1Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
2Center of Excellence on Modelling and Control Systems, Ferdowsi University of Mashhad, Mashhad, Iran
3Department of Mathematics, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Received 1 January 2013; Revised 4 March 2013; Accepted 4 March 2013

Academic Editor: Carlos Vazquez

Copyright © 2013 F. Toutounian 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

This paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized Pantograph equations with variable coefficients by using Legendre Gauss collocation nodes. In the case of numerical solution of Pantograph equation, an error problem is constructed by means of the residual function and this error problem is solved by using the mentioned collocation scheme. When the exact solution of the problem is not known, the absolute errors can be computed approximately by the numerical solution of the error problem. The reliability and efficiency of the presented approaches are demonstrated by several numerical examples, and also the results are compared with different methods.