@Article{AAMM-9-2,
author = {Yan, Jinliang and Ming-Chih, Lai and Zhilin, Li and Zhiyue, Zhang},
title = {New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {2},
pages = {250--271},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2014.m888},
url = {https://global-sci.com/article/73249/new-conservative-finite-volume-element-schemes-for-the-modified-regularized-long-wave-equation}
}