New Preprint ‘Functional-preserving predictor-corrector multiderivative schemes’

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Jochen Schütz, Eleni Theodosiou, and I have published our new preprint Functional-preserving predictor-corrector multiderivative schemes.

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