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 language | English |
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Article number | 112 |
Journal | Mathematical and Computational Applications |
Volume | 29 |
Issue number | 6 |
DOIs | |
Publication status | Published - Dec 2024 |
Externally published | Yes |
Keywords
- Boussinesq equation
- conservation
- convergence
- stability