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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MDPI AG
2024-11-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/29/6/112 |
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| _version_ | 1846103825183670272 |
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| author | Xiaofeng Wang Weizhong Dai Anjan Biswas |
| author_facet | Xiaofeng Wang Weizhong Dai Anjan Biswas |
| author_sort | Xiaofeng Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e4174d0319bb4d41a209d6b0438fc64a |
| institution | Kabale University |
| issn | 1300-686X 2297-8747 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj-art-e4174d0319bb4d41a209d6b0438fc64a2024-12-27T14:38:27ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472024-11-0129611210.3390/mca29060112A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface TensionXiaofeng Wang0Weizhong Dai1Anjan Biswas2School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, ChinaMathematics & Statistics, College of Engineering & Science, Louisiana Tech University, Ruston, LA 71272, USADepartment of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USAIn 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.https://www.mdpi.com/2297-8747/29/6/112Boussinesq equationconvergenceconservationstability |
| spellingShingle | Xiaofeng Wang Weizhong Dai Anjan Biswas A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension Mathematical and Computational Applications Boussinesq equation convergence conservation stability |
| title | A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension |
| title_full | A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension |
| title_fullStr | A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension |
| title_full_unstemmed | A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension |
| title_short | A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension |
| title_sort | conservative and compact finite difference scheme for the sixth order boussinesq equation with surface tension |
| topic | Boussinesq equation convergence conservation stability |
| url | https://www.mdpi.com/2297-8747/29/6/112 |
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