Strong Stability Preserving General Linear Methods

Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

We investigate the strong stability preserving (SSP) general linear methods with two and three external stages and s internal stages. We also describe the construction of starting procedures for these methods. Examples of SSP methods are derived of order p=2,p=3, and p=4 with 2≤s≤10 stages, which have larger effective Courant–Friedrichs–Levy coefficients than the class of two-step Runge–Kutta methods introduced by Jackiewicz and Tracogna, whose SSP properties were analyzes recently by Ketcheson, Gottlieb, and MacDonald, and the class of multistep multistage methods investigated by Constantinescu and Sandu. Numerical examples illustrate that the class of methods derived in this paper achieve the expected order of accuracy and do not produce spurious oscillations for discretizations of hyperbolic conservation laws, when combined with appropriate discretizations in spatial variables.

Original languageEnglish (US)
Pages (from-to)271-298
Number of pages28
JournalJournal of Scientific Computing
Volume65
Issue number1
DOIs
StatePublished - Oct 13 2015

Keywords

  • Courant–Friedrichs–Levy condition
  • General linear methods
  • Monotonicity
  • Multistep multistage methods
  • Shu–Osher representation
  • Strong stability preserving
  • Two-step Runge–Kutta methods

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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