Dense Output for Strong Stability Preserving Runge–Kutta Methods

David I. Ketcheson, Lajos Loczi, Aliya Jangabylova, Adil Kusmanov

Research output: Contribution to journalArticlepeer-review

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Abstract

We investigate dense output formulae (also known as continuous extensions) for strong stability preserving (SSP) Runge–Kutta methods. We require that the dense output formula also possess the SSP property, ideally under the same step-size restriction as the method itself. A general recipe for first-order SSP dense output formulae for SSP methods is given, and second-order dense output formulae for several optimal SSP methods are developed. It is shown that SSP dense output formulae of order three and higher do not exist, and that in any method possessing a second-order SSP dense output, the coefficient matrix A has a zero row.
Original languageEnglish (US)
Pages (from-to)944-958
Number of pages15
JournalJournal of Scientific Computing
Volume71
Issue number3
DOIs
StatePublished - Dec 10 2016

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