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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 596406, 15 pages
http://dx.doi.org/10.1155/2014/596406
Research Article

An Efficient Approach to Numerical Study of the MRLW Equation with B-Spline Collocation Method

1Nevsehir Haci Bektas Veli University, 50300 Nevsehir, Turkey
2Armutlu Vocational High School, Yalova University, 77500 Yalova, Turkey
3Faculty of Computer Science, Abdullah Gül University, 38039 Kayseri, Turkey

Received 1 January 2014; Revised 15 May 2014; Accepted 8 July 2014; Published 22 July 2014

Academic Editor: Ahmet Yasar Ozban

Copyright © 2014 Seydi Battal Gazi Karakoç 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

A septic B-spline collocation method is implemented to find the numerical solution of the modified regularized long wave (MRLW) equation. Three test problems including the single soliton and interaction of two and three solitons are studied to validate the proposed method by calculating the error norms and and the invariants , , and . Also, we have studied the Maxwellian initial condition pulse. The numerical results obtained by the method show that the present method is accurate and efficient. Results are compared with some earlier results given in the literature. A linear stability analysis of the method is also investigated.