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

Yan, J. L. ; Zheng, L. H.

International Journal of Applied Mathematics and Computer Science, Tome 27 (2017) no. 3, pp. 515-525.

Résumé

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.

Détail

Keywords: mass, energy, momentum, finite volume method, Korteweg–de Vries equation
Mots-clés : pęd, metoda objętości skończonych, równanie Kortewega-de Vries

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