Skip to main content
×
Home
    • Aa
    • Aa

New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation

  • Jinliang Yan (a1) (a2), Ming-Chih Lai (a3), Zhilin Li (a4) and Zhiyue Zhang (a1)
Abstract
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.

Copyright
Corresponding author
*Corresponding author. Email:zhangzhiyue@njnu.edu.cn (Z. Y. Zhang)
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[3] D.Furihata and T.Matsuo , Discrete Variational Derivative Method: A Structure-Preserving Numerical Method for Partial Differential Equations, CRC Press, London, 2010.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords: