A High Order IMEX Method for Generalized Korteweg de-Vries Equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917962012688384 |
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| author | Gerberding, Seth |
| author_facet | Gerberding, Seth |
| contents | In this paper, we introduce a high order space-time approximation of generalized Korteweg de-Vries equations. More specifically, the method uses continuous $H^1$-conforming finite elements for the spatial approximation and implicit-explicit methods for the temporal approximation. The method is high order in both space, provably stable, and mass-conservative. The scheme is formulated, its properties are proven, and numerical simulations are provided to illustrate the proposed methodology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A High Order IMEX Method for Generalized Korteweg de-Vries Equations Gerberding, Seth Numerical Analysis In this paper, we introduce a high order space-time approximation of generalized Korteweg de-Vries equations. More specifically, the method uses continuous $H^1$-conforming finite elements for the spatial approximation and implicit-explicit methods for the temporal approximation. The method is high order in both space, provably stable, and mass-conservative. The scheme is formulated, its properties are proven, and numerical simulations are provided to illustrate the proposed methodology. |
| title | A High Order IMEX Method for Generalized Korteweg de-Vries Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2503.15397 |