English

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}
}