Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms
Type
ArticleAuthors
Ketcheson, David I.
KAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2019-12-12Permanent link to this record
http://hdl.handle.net/10754/659994
Metadata
Show full item recordAbstract
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.Citation
Ketcheson, D. I. (2019). Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms. SIAM Journal on Numerical Analysis, 57(6), 2850–2870. doi:10.1137/19m1263662Sponsors
The author is grateful to Hendrik Ranocha for helpful comments on drafts of this work.arXiv
1905.09847Additional Links
https://epubs.siam.org/doi/10.1137/19M1263662ae974a485f413a2113503eed53cd6c53
10.1137/19m1263662