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arXiv · 2308.04876

Functional-preserving predictor-corrector multiderivative schemes

Hendrik Ranocha·Jochen Schütz·Eleni Theodosiou
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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.

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Hendrik Ranocha, Jochen Schütz, Eleni Theodosiou. 2023-08-09. Functional-preserving predictor-corrector multiderivative schemes. https://doi.org/10.1002/pamm.202300025

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