Year: 2017
Author: Jinliang Yan, Ming-Chih Lai, Zhilin Li, Zhiyue Zhang
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 2 : pp. 250–271
Abstract
In this paper, we propose a new energy-preserving scheme and a new momentum-preserving scheme for the modified regularized long wave equation. The proposed schemes are designed by using the discrete variational derivative method and the finite volume element method. For comparison, we also propose a finite volume element scheme. The conservation properties of the proposed schemes are analyzed and we find that the energy-preserving scheme can precisely conserve the discrete total mass and total energy, the momentum-preserving scheme can precisely conserve the discrete total mass and total momentum, while the finite volume element scheme merely conserve the discrete total mass. We also analyze their linear stability property using the Von Neumann theory and find that the proposed schemes are unconditionally linear stable. Finally, we present some numerical examples to illustrate the effectiveness of the proposed schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2014.m888
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 2 : pp. 250–271
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Energy momentum mass finite volume element method MRLW equation.
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