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arxiv: 1905.09847 · v1 · pith:6GRGKDFSnew · submitted 2019-05-23 · 🧮 math.NA

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

David I. Ketcheson This is my paper
classification 🧮 math.NA
keywords methodsstabilityconservationinner-productmodifiedpropertiesrunge--kuttaaccuracy
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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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