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)|
|Number of pages||21|
|Journal||SIAM Journal on Numerical Analysis|
|State||Published - Dec 12 2019|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The author is grateful to Hendrik Ranocha for helpful comments on drafts of this work.