A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension

Xiaofeng Wang*, Weizhong Dai, Anjan Biswas

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this study, we propose a conservative and compact finite difference scheme designed to preserve both the mass change rate and energy for solving the sixth-order Boussinesq equation with surface tension. Theoretical analysis confirms that the proposed scheme achieves second-order accuracy in temporal discretization and fourth-order accuracy in spatial discretization. The solvability, convergence, and stability of the difference scheme are rigorously established through the application of the discrete energy method. Additionally, a series of numerical experiments are conducted to illustrate the effectiveness and reliability of the conservative scheme for long-time simulations.

Original languageEnglish
Article number112
JournalMathematical and Computational Applications
Volume29
Issue number6
DOIs
Publication statusPublished - Dec 2024
Externally publishedYes

Keywords

  • Boussinesq equation
  • conservation
  • convergence
  • stability

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