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 language||English (US)|
|Number of pages||15|
|Journal||Journal of Scientific Computing|
|State||Published - Dec 10 2016|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Adil Kusmanov: This work was supported by the King Abdullah University of Science and Technology (KAUST), 4700 Thuwal, 23955-6900, Saudi Arabia. The second author was also supported by the Department of Numerical Analysis, Eötvös Loránd University, and the Department of Differential Equations, Budapest University of Technology and Economics, Hungary. The last two authors were supported by the KAUST Visiting Student Research Program.