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

Jin-Liang Yan; Liang-Hong Zheng

doi:10.1515/amcs-2017-0036

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

International Journal of Applied Mathematics and Computer Science

Volume 27 (2017): Issue 3 (September 2017)

By: Jin-Liang Yan and Liang-Hong Zheng

Open Access

|Sep 2017

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.

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Articles in this issue

DOI: https://doi.org/10.1515/amcs-2017-0036 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X

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Language: English

Page range: 515 - 525

Submitted on: Oct 22, 2016

Accepted on: Apr 10, 2017

Published on: Sep 23, 2017

Published by: University of Zielona Góra

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

mass,

energy,

momentum,

finite volume element method,

complex modified Korteweg–de Vries equation

Related subjects:

Mathematics,

Applied mathematics

© 2017 Jin-Liang Yan, Liang-Hong Zheng, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 27 (2017): Issue 3 (September 2017)