Journal of Ocean Engineering and Science

Volume 3, Issue 1

(7)A numerical technique based on collocation method for solving modified Kawahara equation

Turgut Ak ^{a , ∗,}S. Battal Gazi Karakoc^ba Department of Transportation Engineering, Yalova University, Yalova, 77200 Turkey

b Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University, Nevsehir, 50300 Turkey

Received 21 November 2017; received in revised form 14 December 2017; accepted 25 December 2017
Available online 5 January 2018

Abstract
In this article, a numerical solution of the modified Kawahara equation is presented by septic B-spline collocation method. Applying the von-Neumann stability analysis, the present method is shown to be unconditionally stable. L 2 and L ∞ error norms and conserved quantities are given at selected times. The accuracy of the proposed method is checked by test problems including motion of the single solitary wave, interaction of solitary waves and evolution of solitons.
© 2018 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Keywords: Modified Kawahara equation; Finite element method; Collocation; Solitary waves; B-spline.