<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg–de Vries equation. The method is based on a combination of a discrete variational derivative method in time and finite volume element approximation in space. The resulting scheme is accurate, robust and energy-preserving. In addition, for comparison, we also develop a momentum-preserving finite volume element scheme and an implicit midpoint finite volume element scheme. Finally, a complete numerical study is developed to investigate the accuracy, conservation properties and long time behaviors of the energy-preserving scheme, in comparison with the momentum-preserving scheme and the implicit midpoint scheme, for the complex modified Korteweg–de Vries equation.</p></abstract>

The aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg–de Vries equation. The method is based on a combination of a discrete variational derivative method in time and finite volume element approximation in space. The resulting scheme is accurate, robust and energy-preserving. In addition, for comparison, we also develop a momentum-preserving finite volume element scheme and an implicit midpoint finite volume element scheme. Finally, a complete numerical study is developed to investigate the accuracy, conservation properties and long time behaviors of the energy-preserving scheme, in comparison with the momentum-preserving scheme and the implicit midpoint scheme, for the complex modified Korteweg–de Vries equation.

Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation

International Journal of Applied Mathematics and Computer Science

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

The aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg–de Vries equation. The method is...

Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation

Published Online: Sep 23, 2017

Page range: 515 - 525

Received: Oct 22, 2016

Accepted: Apr 10, 2017

DOI: https://doi.org/10.1515/amcs-2017-0036

Keywords
mass, energy, momentum, finite volume element method, complex modified Korteweg–de Vries equation

© 2017 Jin-Liang Yan et al., published by De Gruyter Open

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

Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation

Published Online: Sep 23, 2017

Page range: 515 - 525

Received: Oct 22, 2016

Accepted: Apr 10, 2017

DOI: https://doi.org/10.1515/amcs-2017-0036

Keywordsmass, energy, momentum, finite volume element method, complex modified Korteweg–de Vries equation

© 2017 Jin-Liang Yan et al., published by De Gruyter Open

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

Keywords
mass, energy, momentum, finite volume element method, complex modified Korteweg–de Vries equation