Strong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order

Yiannis Hadjimichael, Colin B. MacDonald, David I. Ketcheson, James H. Verner

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge--Kutta methods. Relative to classical Runge--Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods---like classical order five methods---require the use of nonpositive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge--Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.
Original languageEnglish (US)
Pages (from-to)2149-2165
Number of pages17
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number4
DOIs
StatePublished - Jul 23 2013

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