The SBP-SAT technique for initial value problems

Tomas Lundquist, Jan Nordström

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)

Abstract

A detailed account of the stability and accuracy properties of the SBP-SAT technique for numerical time integration is presented. We show how the technique can be used to formulate both global and multi-stage methods with high order of accuracy for both stiff and non-stiff problems. Linear and non-linear stability results, including A-stability, L-stability and B-stability are proven using the energy method for general initial value problems. Numerical experiments corroborate the theoretical properties.

Original languageEnglish
Pages (from-to)86-104
Number of pages19
JournalJournal of Computational Physics
Volume270
DOIs
Publication statusPublished - 1 Aug 2014
Externally publishedYes

Keywords

  • Boundary conditions
  • Convergence
  • Global methods
  • High order accuracy
  • Initial boundary value problems
  • Initial value problems
  • Stability
  • Stiff problems
  • Summation-by-parts operators
  • Time integration

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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