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

Yan, Jin-Liang; Zheng, Liang-Hong

doi:10.1515/amcs-2017-0036

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

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