<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov–Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.</p></abstract>

The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov–Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.

A finite element method for extended KdV equations

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra,

Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra,

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A finite element method for extended KdV equations"}

The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak...

A finite element method for extended KdV equations

Published Online: Sep 29, 2016

Page range: 555 - 567

Received: Jun 02, 2015

Accepted: Mar 08, 2016

DOI: https://doi.org/10.1515/amcs-2016-0039

Keywords
shallow water wave problem, nonlinear equations, second order KdV equations, finite element method, Petrov–Galerkin method

© 2016 Anna Karczewska et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A finite element method for extended KdV equations

Published Online: Sep 29, 2016

Page range: 555 - 567

Received: Jun 02, 2015

Accepted: Mar 08, 2016

DOI: https://doi.org/10.1515/amcs-2016-0039

Keywordsshallow water wave problem, nonlinear equations, second order KdV equations, finite element method, Petrov–Galerkin method

© 2016 Anna Karczewska et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
shallow water wave problem, nonlinear equations, second order KdV equations, finite element method, Petrov–Galerkin method