The Mathematical Institute, University of Oxford, Eprints Archive

Strong Stability Preserving Two-Step Runge-Kutta Methods

Ketcheson, D. I. and Gottlieb, S. and Macdonald, C. B. (2011) Strong Stability Preserving Two-Step Runge-Kutta Methods. SIAM Journal on Numerical Analysis . (Submitted)

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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 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 WENO discretizations.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1259
Deposited By:Peter Hudston
Deposited On:26 May 2011 07:45
Last Modified:09 Feb 2012 14:04

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