Dense Output for Strong Stability Preserving Runge–Kutta Methods

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

doi:10.1007/s10915-016-0331-5

Dense Output for Strong Stability Preserving Runge–Kutta Methods

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

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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 language	English (US)
Pages (from-to)	944-958
Number of pages	15
Journal	Journal of Scientific Computing
Volume	71
Issue number	3
DOIs	https://doi.org/10.1007/s10915-016-0331-5
State	Published - Dec 10 2016

Bibliographical note

KAUST 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.

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title = "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.",

author = "Ketcheson, {David I.} and Lajos Loczi and Aliya Jangabylova and Adil Kusmanov",

note = "KAUST 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, E{\"o}tv{\"o}s Lor{\'a}nd 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.",

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doi = "10.1007/s10915-016-0331-5",

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T1 - Dense Output for Strong Stability Preserving Runge–Kutta Methods

AU - Ketcheson, David I.

AU - Loczi, Lajos

AU - Jangabylova, Aliya

AU - Kusmanov, Adil

N1 - KAUST 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.

PY - 2016/12/10

Y1 - 2016/12/10

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/622186

UR - http://link.springer.com/article/10.1007%2Fs10915-016-0331-5

UR - http://www.scopus.com/inward/record.url?scp=85006356479&partnerID=8YFLogxK

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VL - 71

SP - 944

EP - 958

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

ER -

Dense Output for Strong Stability Preserving Runge–Kutta Methods

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