Dirk schemes with high weak stage order

Document Type

Conference Proceeding

Publication Date

1-1-2020

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.

Identifier

85089721283 (Scopus)

ISBN

[9783030396466]

Publication Title

Lecture Notes in Computational Science and Engineering

External Full Text Location

https://doi.org/10.1007/978-3-030-39647-3_36

e-ISSN

21977100

ISSN

14397358

First Page

453

Last Page

463

Volume

134

Grant

DMS-1719693

Fund Ref

National Science Foundation

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