Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 824167, 13 pages
http://dx.doi.org/10.1155/2011/824167
Research Article

Legendre Polynomials Spectral Approximation for the Infinite-Dimensional Hamiltonian Systems

Zhongquan Lv,1,2 Mei Xue,1 and Yushun Wang1

1Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China
2College of Science, Nanjing Forestry University, Nanjing 210037, China

Received 11 October 2010; Revised 6 April 2011; Accepted 30 April 2011

Academic Editor: Paulo Batista Gonçalves

Copyright © 2011 Zhongquan Lv 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 considers a Legendre polynomials spectral approximation for the infinite-dimensional Hamiltonian systems. As a consequence, the Legendre polynomials spectral semidiscrete system is a Hamiltonian system for the Hamiltonian system whose Hamiltonian operator is a constant differential operator.