Eur. Phys. J. Plus (2016) 131: 356
https://doi.org/10.1140/epjp/i2016-16356-3

Regular Article

Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation

¹ Faculty of Engineering, Department of Transportation Engineering, Yalova University, 77100, Yalova, Turkey
² Faculty of Science and Art, Department of Mathematics, Nevsehir Haci Bektas Veli University, 50300, Nevsehir, Turkey
³ Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 23000, Annaba, Algeria

^* e-mail: akturgut@yahoo.com

Received: 23 May 2016
Accepted: 13 September 2016
Published online: 12 October 2016

Abstract

In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated solitary waves of different amplitudes, evolution of solitons with Gaussian and undular bore initial conditions are obtained. Stability and a priori error estimate of the scheme are discussed. A comparison of the values of the obtained invariants and error norms for single solitary wave with earlier results is also made. The results show that the present method is efficient and reliable.