Journal of Scientific Computing

, Volume 71, Issue 3, pp 944–958 | Cite as

Dense Output for Strong Stability Preserving Runge–Kutta Methods

  • David I. KetchesonEmail author
  • Lajos Lóczi
  • Aliya Jangabylova
  • Adil Kusmanov


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.


Runge-Kutta methods SSP methods Dense output Continuous extension 



We thank an anonymous referee for several suggestions that improved the presentation of this work.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • David I. Ketcheson
    • 1
    Email author
  • Lajos Lóczi
    • 1
  • Aliya Jangabylova
    • 2
  • Adil Kusmanov
    • 2
  1. 1.King Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia
  2. 2.Nazarbayev UniversityAstanaKazakhstan

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