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

1 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 languageEnglish (US)
Title of host publicationLecture Notes in Computational Science and Engineering
PublisherSpringer International Publishing
Pages453-463
Number of pages11
ISBN (Print)9783030396466
DOIs
StatePublished - Aug 11 2020

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