Canonical Runge-Kutta methods

  • F. M. Lasagni
Brief Reports


In the present note we provide a complete characterization of all Runge-Kutta methods which generate a canonical transformation if applied to a Hamiltonian system of ordinary differential equations.


  1. [1]
    V. I. Arnold (Ed.), Dynamical Systems III. Encyclopedia of Mathematical Sciences Vol. 3. Springer-Verlag, Berlin, Heidelberg, 1988.Google Scholar
  2. [2]
    Feng Kang, Difference schemes for Hamiltonian formalism and sympiectic geometry. J. of Comp. Math.,4, 279–289 (1986).Google Scholar
  3. [3]
    E. Hairer, Algebraically stable and implementable Runge-Kutta methods of high-order. SIAM J. Numer. Anal.,18, No. 6, 1981.Google Scholar
  4. [4]
    E. Hairer, S. P. Norsett, G. Wanner, Solving ordinary differential equations I. Springer Series in Computational Math.,8, 1987.Google Scholar
  5. [5]
    F. C. Iselin, Algorithms for Tracking Charged Particles in Circular Accelerators. Lect. Notes in Physics, 247, Springer, Berlin, 1986.Google Scholar
  6. [6]
    D. M. Stoffer, Some geometric and numerical methods for perturbed integrated systems. Diss. ETH, No. 8456, Zürich, 1988.Google Scholar
  7. [7]
    F. M. Lasagni, in preparation, to appear in Numerische Mathematik.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1988

Authors and Affiliations

  • F. M. Lasagni
    • 1
  1. 1.MathematicsETHZürich

Personalised recommendations