BIT Numerical Mathematics

, Volume 38, Issue 4, pp 802–806 | Cite as

A note on pseudo-symplectic Runge-Kutta methods

  • A. Aubry
  • P. Chartier
Scientific Notes


Aubry and Chartier introduced (1998) the concept of pseudo-symplecticness in order to construct explicit Runge-Kutta methods, which mimic symplectic ones. Of particular interest are methods of order (p, 2p), i.e., of orderp and pseudo-symplecticness order 2p, for which the growth of the global error remains linear. The aim of this note is to show that the lower bound for the minimal number of stages can be achieved forp=4 andp=5.

AMS subject classification


Key words

Hamiltonian systems pseudo-symplecticness conditions tensor products 


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  1. 1.
    A. Aubry and P. Chartier,Pseudo-symplectic Runge-Kutta methods, BIT, 38:3 (1998), pp. 439–461.MATHMathSciNetGoogle Scholar
  2. 2.
    J. C. Butcher,The Numerical Analysis of Ordinary Differential Equations, Wiley, 1987.Google Scholar
  3. 3.
    E. Hairer, S. P. Nørsett, and G. Wanner,Solving Ordinary Differential Equations I. Nonstiff Problems, 2nd ed., Springer-Verlag, Berlin, 1993.MATHGoogle Scholar

Copyright information

© Swets & Zeitlinger 1998

Authors and Affiliations

  • A. Aubry
    • 1
  • P. Chartier
    • 1
  1. 1.Campus de BeaulieuIRISARennes CedexFrance

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