Dense Output for Strong Stability Preserving Runge–Kutta Methods

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.

Citation
Ketcheson DI, Lóczi L, Jangabylova A, Kusmanov A (2016) Dense Output for Strong Stability Preserving Runge–Kutta Methods. Journal of Scientific Computing. Available: http://dx.doi.org/10.1007/s10915-016-0331-5.

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.

Publisher
Springer Nature

Journal
Journal of Scientific Computing

DOI
10.1007/s10915-016-0331-5

arXiv
1605.02429

Additional Links
http://link.springer.com/article/10.1007%2Fs10915-016-0331-5https://arxiv.org/abs/1605.02429

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