Functional-preserving predictor-corrector multiderivative schemes
Abstract
In this work, we develop a class of high-order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recently developed Hermite-Birkhoff-Predictor-Corrector methods and the technique of relaxation for numerical methods of ODEs. We explain the algorithm in detail and show numerical results for two- and three-derivative methods, comparing relaxed and unrelaxed methods. The numerical results demonstrate that, at the slight cost of the relaxation, an improved scheme is obtained.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2023
- DOI:
- 10.48550/arXiv.2308.04876
- arXiv:
- arXiv:2308.04876
- Bibcode:
- 2023arXiv230804876R
- Keywords:
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- Mathematics - Numerical Analysis
- E-Print:
- Submitted to the Proceedings in Applied Mathematics and Mechanic (GAMM Annual Meeting 2023)