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 Citations (Scopus)


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
Article number33
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - Apr 2021


  • A stability
  • Energy stability
  • Projection method
  • Runge–Kutta methods
  • Summation by parts
  • Time integration schemes

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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