Relaxation Runge-Kutta Methods: Conservation and stability for Inner-Product Norms
Numerical Analysis
2019-05-27 v1
Abstract
We further develop a simple modification of Runge--Kutta methods that guarantees conservation or stability with respect to any inner-product norm. The modified methods can be explicit and retain the accuracy and stability properties of the unmodified Runge--Kutta method. We study the properties of the modified methods and show their effectiveness through numerical examples, including application to entropy-stability for first-order hyperbolic PDEs.
Keywords
Cite
@article{arxiv.1905.09847,
title = {Relaxation Runge-Kutta Methods: Conservation and stability for Inner-Product Norms},
author = {David I. Ketcheson},
journal= {arXiv preprint arXiv:1905.09847},
year = {2019}
}