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Title: | Multiderivative time integration methods preserving nonlinear functionals via relaxation | Authors: | Ranocha, Hendrik SCHUETZ, Jochen |
Issue Date: | 2024 | Publisher: | Source: | Communications in Applied Mathematics and Computational Science, 19 (1) , p. 27 -56 | Status: | Early view | Abstract: | 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. | Keywords: | two-derivative methods;multiderivative methods;invariants;conservative systems;dissipative systems;structure-preserving methods AMS subject classification 65L06;65M20;65M70 | Document URI: | http://hdl.handle.net/1942/43295 | ISSN: | 1559-3940 | e-ISSN: | 2157-5452 | DOI: | 10.2140/camcos.2024.19.27 | Rights: | 2024 MSP (Mathematical Sciences Publishers). | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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multiderivative_relaxation__arXiv.pdf Restricted Access | Early view | 1.12 MB | Adobe PDF | View/Open Request a copy |
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