Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms
AuthorsKetcheson, David I.
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/659994
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AbstractWe 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.
CitationKetcheson, D. I. (2019). Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms. SIAM Journal on Numerical Analysis, 57(6), 2850–2870. doi:10.1137/19m1263662
SponsorsThe author is grateful to Hendrik Ranocha for helpful comments on drafts of this work.