New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we propose a new energy-preserving scheme and a newmomentum-preserving scheme for the modified regularized long wave equation. Theproposed schemes are designed by using the discrete variational derivative methodand the finite volume element method. For comparison, we also propose a finitevolume element scheme. The conservation properties of the proposed schemes areanalyzed and we find that the energy-preserving scheme can precisely conserve thediscrete total mass and total energy, the momentum-preserving scheme can preciselyconserve the discrete total mass and total momentum, while the finite volume elementscheme merely conserve the discrete total mass. We also analyze their linear stabilityproperty using the Von Neumann theory and find that the proposed schemes are unconditionallylinear stable. Finally, we present some numerical examples to illustratethe effectiveness of the proposed schemes.