A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation
In this article, a numerical solution for the Rosenau-Kawahara equation is considered. A new conservative numerical approximation scheme is presented to solve the initial boundary value problem of the Rosenau-Kawahara equation, which preserves the original conservative properties. The proposed schem...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-05-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0204 |
| _version_ | 1797816752836444160 |
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| author | Pan Xintian Zhang Luming |
| author_facet | Pan Xintian Zhang Luming |
| author_sort | Pan Xintian |
| collection | DOAJ |
| description | In this article, a numerical solution for the Rosenau-Kawahara equation is considered. A new conservative numerical approximation scheme is presented to solve the initial boundary value problem of the Rosenau-Kawahara equation, which preserves the original conservative properties. The proposed scheme is based on the finite difference method. The existence of the numerical solutions for the scheme has been shown by Browder fixed point theorem. The priori bound and error estimates, as well as the conservation of discrete mass and discrete energy for the finite difference solutions, are discussed. The discrepancies of discrete mass and energy are computed and shown by the curves of these quantities over time. Unconditional stability, second-order convergence, and uniqueness of the scheme are proved based on the discrete energy method. Numerical examples are given to show the effectiveness of the proposed scheme and confirm the theoretical analysis. |
| first_indexed | 2024-03-13T08:42:21Z |
| format | Article |
| id | doaj.art-bb0912ce3cd14efd9af9c82c96f0f494 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-03-13T08:42:21Z |
| publishDate | 2023-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-bb0912ce3cd14efd9af9c82c96f0f4942023-05-30T09:12:52ZengDe GruyterDemonstratio Mathematica2391-46612023-05-0156165766210.1515/dema-2022-0204A novel conservative numerical approximation scheme for the Rosenau-Kawahara equationPan Xintian0Zhang Luming1School of Mathematics and Information Science, Weifang University, Weifang, 261061, ChinaDepartment of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, ChinaIn this article, a numerical solution for the Rosenau-Kawahara equation is considered. A new conservative numerical approximation scheme is presented to solve the initial boundary value problem of the Rosenau-Kawahara equation, which preserves the original conservative properties. The proposed scheme is based on the finite difference method. The existence of the numerical solutions for the scheme has been shown by Browder fixed point theorem. The priori bound and error estimates, as well as the conservation of discrete mass and discrete energy for the finite difference solutions, are discussed. The discrepancies of discrete mass and energy are computed and shown by the curves of these quantities over time. Unconditional stability, second-order convergence, and uniqueness of the scheme are proved based on the discrete energy method. Numerical examples are given to show the effectiveness of the proposed scheme and confirm the theoretical analysis.https://doi.org/10.1515/dema-2022-0204rosenau-kawahara equationconservative difference schemeexistenceconvergence65n0665n12 |
| spellingShingle | Pan Xintian Zhang Luming A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation Demonstratio Mathematica rosenau-kawahara equation conservative difference scheme existence convergence 65n06 65n12 |
| title | A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation |
| title_full | A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation |
| title_fullStr | A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation |
| title_full_unstemmed | A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation |
| title_short | A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation |
| title_sort | novel conservative numerical approximation scheme for the rosenau kawahara equation |
| topic | rosenau-kawahara equation conservative difference scheme existence convergence 65n06 65n12 |
| url | https://doi.org/10.1515/dema-2022-0204 |
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