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New conservative finite volume element schemes for the modified Korteweg–de Vries equation
Author(s) -
Yan Jinliang,
Zhang Qian,
Zhang Zhiyue
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3896
Subject(s) - mathematics , finite element method , korteweg–de vries equation , finite volume method , mathematical analysis , derivative (finance) , stability (learning theory) , boundary value problem , volume (thermodynamics) , nonlinear system , mechanics , physics , computer science , quantum mechanics , machine learning , financial economics , economics , thermodynamics
In this paper, three conservative finite volume element schemes are proposed and compared for the modif ied Korteweg–de Vries equation, especially with regard to their accuracy and conservative properties. The schemes are constructed basing on the discrete variational derivative method and the finite volume element method to inherit the properties of the original equation. The theoretical analysis show that three schemes are conservative under suitable boundary conditions as well as unconditionally linear stability. Numerical experiments are given to confirm the theoretical results and the capacity of the proposed methods for capturing the solitary wave phenomena. Copyright © 2016 John Wiley & Sons, Ltd.