Table of Contents
International Journal of Partial Differential Equations
Volume 2014, Article ID 343497, 8 pages
http://dx.doi.org/10.1155/2014/343497
Research Article

Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

Department of Mathematics, IIT Roorkee, Roorkee, Uttarakhand 247667, India

Received 11 May 2014; Accepted 16 July 2014; Published 10 August 2014

Academic Editor: Nikolai A. Kudryashov

Copyright © 2014 R. C. Mittal and Rachna Bhatia. 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

Modified cubic B-spline collocation method is discussed for the numerical solution of one-dimensional nonlinear sine-Gordon equation. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. The given equation is decomposed into a system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of ordinary differential equations. The resulting system of equation has subsequently been solved by SSP-RK54 scheme. The efficacy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and are in good agreement with earlier studies.