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

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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 languageEnglish (US)
Pages (from-to)2850-2870
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume57
Issue number6
DOIs
StatePublished - Dec 12 2019

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