A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions

Hendrik Ranocha, Jan Nordström

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Since integration by parts is an important tool when deriving energy or entropy estimates for differential equations, one may conjecture that some form of summation by parts (SBP) property is involved in provably stable numerical methods. This article contributes to this topic by proposing a novel class of A stable SBP time integration methods which can also be reformulated as implicit Runge-Kutta methods. In contrast to existing SBP time integration methods using simultaneous approximation terms to impose the initial condition weakly, the new schemes use a projection method to impose the initial condition strongly without destroying the SBP property. The new class of methods includes the classical Lobatto IIIA collocation method, not previously formulated as an SBP scheme. Additionally, a related SBP scheme including the classical Lobatto IIIB collocation method is developed.
Original languageEnglish (US)
JournalJournal of Scientific Computing
Issue number1
StatePublished - Mar 10 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-03-12
Acknowledgements: Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Jan Nordström was supported by Vetenskapsrådet, Sweden grant 2018-05084 VR and by the Swedish e-Science Research Center (SeRC) through project ABL in SESSI.

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Software
  • General Engineering


Dive into the research topics of 'A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions'. Together they form a unique fingerprint.

Cite this