Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms

David I. Ketcheson

doi:10.1137/19m1263662

Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms

David I. Ketcheson

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English (US)
Pages (from-to)	2850-2870
Number of pages	21
Journal	SIAM Journal on Numerical Analysis
Volume	57
Issue number	6
DOIs	https://doi.org/10.1137/19m1263662
State	Published - Dec 12 2019

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https://repository.kaust.edu.sa/bitstream/10754/659994/4/19m1263662.pdf

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title = "Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms",

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.",

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AB - 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.

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Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms

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