Multiderivative time integration methods preserving nonlinear functionals via relaxation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929390688927744 |
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| author | Ranocha, Hendrik Schütz, Jochen |
| author_facet | Ranocha, Hendrik Schütz, Jochen |
| contents | We combine the recent relaxation approach with multiderivative Runge-Kutta methods to preserve conservation or dissipation of entropy functionals for ordinary and partial differential equations. Relaxation methods are minor modifications of explicit and implicit schemes, requiring only the solution of a single scalar equation per time step in addition to the baseline scheme. We demonstrate the robustness of the resulting methods for a range of test problems including the 3D compressible Euler equations. In particular, we point out improved error growth rates for certain entropy-conservative problems including nonlinear dispersive wave equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_03883 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multiderivative time integration methods preserving nonlinear functionals via relaxation Ranocha, Hendrik Schütz, Jochen Numerical Analysis 65L06, 65M20, 65M70 We combine the recent relaxation approach with multiderivative Runge-Kutta methods to preserve conservation or dissipation of entropy functionals for ordinary and partial differential equations. Relaxation methods are minor modifications of explicit and implicit schemes, requiring only the solution of a single scalar equation per time step in addition to the baseline scheme. We demonstrate the robustness of the resulting methods for a range of test problems including the 3D compressible Euler equations. In particular, we point out improved error growth rates for certain entropy-conservative problems including nonlinear dispersive wave equations. |
| title | Multiderivative time integration methods preserving nonlinear functionals via relaxation |
| topic | Numerical Analysis 65L06, 65M20, 65M70 |
| url | https://arxiv.org/abs/2311.03883 |