Dirk schemes with high weak stage order

Abstract
Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.

Citation
Ketcheson, D. I., Seibold, B., Shirokoff, D., & Zhou, D. (2020). DIRK Schemes with High Weak Stage Order. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, 453–463. doi:10.1007/978-3-030-39647-3_36

Acknowledgements
This work was supported by the National Science Foundation via grants DMS-1719640 (BS&DZ) and DMS-1719693 (DS); and the Simons Foundation (#359610) (DS).

Publisher
Springer Nature

Conference/Event Name
12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018

DOI
10.1007/978-3-030-39647-3_36

arXiv
1811.01285

Additional Links
http://link.springer.com/10.1007/978-3-030-39647-3_36

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