Conservative Finite Difference Method for Solving Generalized BBM-KdV Equation
The BBM-KdV equation plays an important role because it can describe a large number of physical phenomena, such as shallow water waves and ion waves. It is an important model for long-wave unidirectional propagation in weakly nonlinear dispersive media, but its numerical investigations are rarely ma...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | zho |
| Published: |
Harbin University of Science and Technology Publications
2022-08-01
|
| Series: | Journal of Harbin University of Science and Technology |
| Subjects: | |
| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2128 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849713292357926912 |
|---|---|
| author | WANG Xi ZHANG Shuang HU Jin-song |
| author_facet | WANG Xi ZHANG Shuang HU Jin-song |
| author_sort | WANG Xi |
| collection | DOAJ |
| description | The BBM-KdV equation plays an important role because it can describe a large number of physical phenomena, such as shallow water waves and ion waves. It is an important model for long-wave unidirectional propagation in weakly nonlinear dispersive media, but its numerical investigations are rarely made. For the initial-boundary value problem of the generalized BBM-KdV equations with homogeneous boundary conditions, a two-level nonlinear finite difference scheme with the second-order theoretical accuracy is proposed, which reasonably simulates the two conserved quantities of the problem. With a priori estimation, the existence and uniqueness of the difference solutions are dicussed. By the discrete functional analysis method the convergence and unconditional stability of the scheme are also proved. Finally, some numerical experiments verify the robustness of the proposed scheme. |
| format | Article |
| id | doaj-art-560cc313c27f495689da81fe9a645980 |
| institution | DOAJ |
| issn | 1007-2683 |
| language | zho |
| publishDate | 2022-08-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj-art-560cc313c27f495689da81fe9a6459802025-08-20T03:13:59ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832022-08-01270414715310.15938/j.jhust.2022.04.019Conservative Finite Difference Method for Solving Generalized BBM-KdV EquationWANG Xi0ZHANG Shuang1HU Jin-song2School of Science, Xihua University, Chengdu 610039,ChinaSchool of Science, Xihua University, Chengdu 610039,ChinaSchool of Science, Xihua University, Chengdu 610039,ChinaThe BBM-KdV equation plays an important role because it can describe a large number of physical phenomena, such as shallow water waves and ion waves. It is an important model for long-wave unidirectional propagation in weakly nonlinear dispersive media, but its numerical investigations are rarely made. For the initial-boundary value problem of the generalized BBM-KdV equations with homogeneous boundary conditions, a two-level nonlinear finite difference scheme with the second-order theoretical accuracy is proposed, which reasonably simulates the two conserved quantities of the problem. With a priori estimation, the existence and uniqueness of the difference solutions are dicussed. By the discrete functional analysis method the convergence and unconditional stability of the scheme are also proved. Finally, some numerical experiments verify the robustness of the proposed scheme.https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2128generalized bbm-kdv equationdifference schemeconservationconvergencestability |
| spellingShingle | WANG Xi ZHANG Shuang HU Jin-song Conservative Finite Difference Method for Solving Generalized BBM-KdV Equation Journal of Harbin University of Science and Technology generalized bbm-kdv equation difference scheme conservation convergence stability |
| title | Conservative Finite Difference Method for Solving Generalized BBM-KdV Equation |
| title_full | Conservative Finite Difference Method for Solving Generalized BBM-KdV Equation |
| title_fullStr | Conservative Finite Difference Method for Solving Generalized BBM-KdV Equation |
| title_full_unstemmed | Conservative Finite Difference Method for Solving Generalized BBM-KdV Equation |
| title_short | Conservative Finite Difference Method for Solving Generalized BBM-KdV Equation |
| title_sort | conservative finite difference method for solving generalized bbm kdv equation |
| topic | generalized bbm-kdv equation difference scheme conservation convergence stability |
| url | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2128 |
| work_keys_str_mv | AT wangxi conservativefinitedifferencemethodforsolvinggeneralizedbbmkdvequation AT zhangshuang conservativefinitedifferencemethodforsolvinggeneralizedbbmkdvequation AT hujinsong conservativefinitedifferencemethodforsolvinggeneralizedbbmkdvequation |