Functional-preserving predictor-corrector multiderivative schemes
Numerical Analysis
2023-09-12 v1 Numerical Analysis
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.
Cite
@article{arxiv.2308.04876,
title = {Functional-preserving predictor-corrector multiderivative schemes},
author = {Hendrik Ranocha and Jochen Schütz and Eleni Theodosiou},
journal= {arXiv preprint arXiv:2308.04876},
year = {2023}
}
Comments
Submitted to the Proceedings in Applied Mathematics and Mechanic (GAMM Annual Meeting 2023)