A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension
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 tempo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
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| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/29/6/112 |
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| Summary: | 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. |
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| ISSN: | 1300-686X 2297-8747 |