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Mathematical Problems in Engineering
Volume 2014, Article ID 383219, 10 pages
Research Article

The Improved Moving Least-Square Ritz Method for the One-Dimensional Sine-Gordon Equation

Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

Received 15 December 2013; Accepted 15 January 2014; Published 23 February 2014

Academic Editor: Zan Zhang

Copyright © 2014 Qi Wei and Rongjun Cheng. 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.


Analysis of the one-dimensional sine-Gordon equation is performed using the improved moving least-square Ritz method (IMLS-Ritz method). The improved moving least-square approximation is employed to approximate the 1D displacement field. A system of discrete equations is obtained by application of the Ritz minimization procedure. The effectiveness and accuracy of the IMLS-Ritz method for the sine-Gordon equation are investigated by numerical examples in this paper.