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Explicit fifth order Runge-Kutta methods with five stages for quadratic ODEs

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

Abstract

It is well-known that there exist no general purpose explicit fifth order five stage Runge-Kutta methods. One may however wonder whether there exist explicit five stage methods which are of fifth order for special kinds of problems, for instance problems y′=f(x, y) where f is an m dimensional vector of polynomials of degree at most d in each of the arguments. It is shown that there exist explicit five stage Runge-Kutta methods for quadratic ODEs (d=2). Solutions are given for the non-confluent case and a numerical example is incorporated.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

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

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