Some Embedded Pairs for Optimal Implicit Strong Stability Preserving Runge–Kutta Methods

  • Imre FeketeEmail author
  • Ákos Horváth
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


We construct specific embedded pairs for second and third order optimal strong stability preserving implicit Runge–Kutta methods with large absolute stability regions. These pairs offer adaptive implementation possibility for strong stability preserving (SSP) methods and maintain their inherent nonlinear stability properties, too.



The project has been supported by the European Union, co-financed by the European Social Fund (EFOP-3.6.3-VEKOP-16-2017-00002).


  1. 1.
    Gottlieb, S.: Strong Stability Preserving Time Discretizations: A Review. ICOSAHOM 2014, pp. 17–30. Springer International Publishing, Cham (2015)Google Scholar
  2. 2.
    Gottlieb, S., Ketcheson, D., Shu, C.-W.: Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations. World Scientific Publishing, Singapore (2011)CrossRefGoogle Scholar
  3. 3.
    Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I. Springer, Berlin (1993)zbMATHGoogle Scholar
  4. 4.
    Ketcheson, D., Macdonald, C., Gottlieb, S.: Optimal Implicit Strong Stability Preserving Runge-Kutta Methods. Appl. Numer. Math. 59(2), 373–392 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of MathematicsEötvös Loránd University, MTA-ELTE Numerical Analysis and Large Networks Research GroupBudapestHungary
  2. 2.Institute of MathematicsEötvös Loránd UniversityBudapestHungary

Personalised recommendations