Evaluation of shallow water waves modelled by the Rosenau-Kawahara equation using pseudo-compact finite difference approach

Abstract

This paper presents a finite difference method for the Rosenau-Kawahara equation, which is performed under pseudo-compactness; this facilitates accuracy improvement. It is shown that the proposed scheme can generate a unique numerical solution with second-order convergence in both space and time and that the solution is stable with respect to $\Vert \cdot {\Vert }_{\mathrm{\infty }}$. Also, it turns out that discrete mass and energy at each time step maintain; hence conservation. To guarantee these theoretical results, some numerical experiments are conducted to show how accurate and efficient the scheme can perform. Furthermore, comparisons between the presented method and some existing ones are provided in order to ensure improvement.

Keywords:

• Rosenau-Kawahara equation
• finite difference method
• convergence
• stability

2020 Mathematics Subject Classifications:

• 65N06
• 65N12

Acknowledgments

This research was supported by Centre of Excellence in Mathematics, The Commission on Higher Education, Thailand; and Chiang Mai University. The first author would like to thank the National Science and Technology Development Agency (NSTDA), Thailand for financial support. The authors would also like to thank P. Charoensawan, K. Poochinapan and B. Wongsaijai for their valuable suggestions and for their help during preparation of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by Centre of Excellence in Mathematics, The Commission on Higher Education, Thailand; National Science and Technology Development Agency, Thailand; and Chiang Mai University.