Dirk schemes with high weak stage order

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


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 languageEnglish (US)
Title of host publicationSpectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference
EditorsSpencer J. Sherwin, Joaquim Peiró, Peter E. Vincent, David Moxey, Christoph Schwab
Number of pages11
ISBN (Print)9783030396466
StatePublished - 2020
Event12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 - London, United Kingdom
Duration: Jul 9 2018Jul 13 2018

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100


Conference12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018
Country/TerritoryUnited Kingdom

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Engineering
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics


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