Strong Stability Preserving General Linear Methods

Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We investigate the strong stability preserving (SSP) general linear methods with two and three external stages and (Formula presented.) internal stages. We also describe the construction of starting procedures for these methods. Examples of SSP methods are derived of order (Formula presented.), and (Formula presented.) with (Formula presented.) 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)
JournalJournal of Scientific Computing
DOIs
StateAccepted/In press - Nov 27 2014

Fingerprint

General Linear Methods
Strong Stability
Discretization
Two-step Method
Hyperbolic Conservation Laws
Conservation
Runge-Kutta Methods
Oscillation
Internal
Numerical Examples
Coefficient
Class

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
  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Engineering(all)

Cite this

Strong Stability Preserving General Linear Methods. / Izzo, Giuseppe; Jackiewicz, Zdzislaw.

In: Journal of Scientific Computing, 27.11.2014.

Research output: Contribution to journalArticle

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