Dirk schemes with high weak stage order

David I. Ketcheson; Benjamin Seibold; David Shirokoff; Dong Zhou

doi:10.1007/978-3-030-39647-3_36

Dirk schemes with high weak stage order

David I. Ketcheson, Benjamin Seibold, David Shirokoff, Dong Zhou

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

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.

Original language	English (US)
Title of host publication	Lecture Notes in Computational Science and Engineering
Publisher	Springer International Publishing
Pages	453-463
Number of pages	11
ISBN (Print)	9783030396466
DOIs	https://doi.org/10.1007/978-3-030-39647-3_36
State	Published - Aug 11 2020

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

https://repository.kaust.edu.sa/bitstream/10754/665186/1/DIRK%20scheme.pdf

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@inproceedings{e1884dd79b7c417a89089df0c38bd26e,

title = "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.",

author = "Ketcheson, {David I.} and Benjamin Seibold and David Shirokoff and Dong Zhou",

note = "KAUST Repository Item: Exported on 2020-10-01 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).",

year = "2020",

month = aug,

day = "11",

doi = "10.1007/978-3-030-39647-3_36",

language = "English (US)",

isbn = "9783030396466",

pages = "453--463",

booktitle = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer International Publishing",

}

TY - GEN

T1 - Dirk schemes with high weak stage order

AU - Ketcheson, David I.

AU - Seibold, Benjamin

AU - Shirokoff, David

AU - Zhou, Dong

N1 - KAUST Repository Item: Exported on 2020-10-01 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).

PY - 2020/8/11

Y1 - 2020/8/11

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/665186

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

UR - http://www.scopus.com/inward/record.url?scp=85089721283&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-39647-3_36

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

M3 - Conference contribution

SN - 9783030396466

SP - 453

EP - 463

BT - Lecture Notes in Computational Science and Engineering

PB - Springer International Publishing

ER -

Dirk schemes with high weak stage order

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