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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 206264, 8 pages
http://dx.doi.org/10.1155/2015/206264
Research Article

Discrete-Time Orthogonal Spline Collocation Method for One-Dimensional Sine-Gordon Equation

1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan 471023, China
2China Investment Securities, Shenzhen, Guangdong 518048, China
3First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong 266061, China

Received 13 September 2015; Revised 23 November 2015; Accepted 1 December 2015

Academic Editor: Pilar R. Gordoa

Copyright © 2015 Xiaoquan Ding 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

We present a discrete-time orthogonal spline collocation scheme for the one-dimensional sine-Gordon equation. This scheme uses Hermite basis functions to approximate the solution throughout the spatial domain on each time level. The convergence rate with order in norm and stability of the scheme are proved. Numerical results are presented and compared with analytical solutions to confirm the accuracy of the presented scheme.