Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 758954, 11 pages
http://dx.doi.org/10.1155/2015/758954
Research Article

Convergent Analysis of Energy Conservative Algorithm for the Nonlinear Schrödinger Equation

1College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2College of Science, Nanjing Forestry University, Nanjing 210037, China
3Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, China

Received 26 September 2014; Accepted 27 February 2015

Academic Editor: Slim Choura

Copyright © 2015 Lv Zhong-Quan 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

Using average vector field method in time and Fourier pseudospectral method in space, we obtain an energy-preserving scheme for the nonlinear Schrödinger equation. We prove that the proposed method conserves the discrete global energy exactly. A deduction argument is used to prove that the numerical solution is convergent to the exact solution in discrete norm. Some numerical results are reported to illustrate the efficiency of the numerical scheme in preserving the energy conservation law.