P-stable mono-implicit Runge-Kutta-Nyström modifications of the Numerov method

  • T. Van Hecke
  • M. Van Daele
  • G. Vanden Berghe
  • H. De Meyer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1196)


We present families of fourth-order mono-implicit Runge-Kutta-Nyström methods. Each member of these families can be considered as a modification of the Numerov method. Some parameters of these new methods are used to optimize the linear stability properties, i.e. to obtain P-stable methods with a minimal phase-lag. Also we show that in some cases there exist P-stable methods with stage-order 3. Since the methods considered are mono-implicit, the computational work needed in each time-step to solve the implicit equations is reduced seriously.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • T. Van Hecke
    • 1
  • M. Van Daele
    • 1
  • G. Vanden Berghe
    • 1
  • H. De Meyer
    • 1
  1. 1.Vakgroep Toegepaste Wiskunde en InformaticaUniversiteit-GentGentBelgium

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