Strong Stability Preserving Two-step Runge–Kutta Methods

David I. Ketcheson, Sigal Gottlieb, Colin B. Macdonald

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

We investigate the strong stability preserving (SSP) property of two-step Runge–Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present explicit TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order weighted essentially non-oscillatory discretizations.
Original languageEnglish (US)
Pages (from-to)2618-2639
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume49
Issue number6
DOIs
StatePublished - Dec 22 2011

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