A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with the Surface Tension
How to cite: Wang, X.; Dai, W.; Biswas, A. A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with the Surface Tension. Preprints 2024, 2024100770. https://doi.org/10.20944/preprints202410.0770.v1 Wang, X.; Dai, W.; Biswas, A. A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with the Surface Tension. Preprints 2024, 2024100770. https://doi.org/10.20944/preprints202410.0770.v1
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 the 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.
Keywords
Boussinesq equation; convergence; conservation; stability
Subject
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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