Share:


Numerical Study of Rosenau-KdV Equation Using Finite Element Method Based on Collocation Approach

    Turgut Ak Affiliation
    ; Sharanjeet Dhawan Affiliation
    ; S. Battal Gazi Karakoc Affiliation
    ; Samir K. Bhowmik Affiliation
    ; Kamal R. Raslan Affiliation

Abstract

In the present paper, a numerical method is proposed for the numerical solution of Rosenau-KdV equation with appropriate initial and boundary conditions by using collocation method with septic B-spline functions on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To check accuracy of the error norms L2 and L are computed. Interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves during the interaction. Furthermore, evolution of solitons is illustrated by undular bore initial condition. These results show that the technique introduced here is suitable to investigate behaviors of shallow water waves.

Keyword : Rosenau-KdV, B-spline, finite element, collocation and dispersive

How to Cite
Ak, T., Dhawan, S., Karakoc, S. B. G., Bhowmik, S. K., & Raslan, K. R. (2017). Numerical Study of Rosenau-KdV Equation Using Finite Element Method Based on Collocation Approach. Mathematical Modelling and Analysis, 22(3), 373-388. https://doi.org/10.3846/13926292.2017.1313329
Published in Issue
May 19, 2017
Abstract Views
183
PDF Downloads
224