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Strong Stability Preserving Two-Step Runge-Kutta Methods

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 b...

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Publication date:
2011-01-01
UUID:
uuid:376def9e-48a7-43cd-a3d1-6c9c62a8c5c6
Local pid:
oai:eprints.maths.ox.ac.uk:1259
Deposit date:
2011-05-31

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