The rate of error growth in Hamiltonian-conserving integrators

  • Donald J. Estep
  • Andrew M. Stuart
Original Papers


In this note, we consider numerical methods for a class of Hamiltonian systems that preserve the Hamiltonian. We show that the rate of growth of error is at most linear in time when such methods are applied to problems with period uniquely determined by the value of the Hamiltonian. This contrasts to generic numerical schemes, for which the rate of error growth is superlinear. Asymptotically, the rate of error growth for symplectic schemes is also linear. Hence, Hamiltonian-conserving schemes are competitive with symplectic schemes in this respect. The theory is illustrated with a computation performed on Kepler's problem for the interaction of two bodies.


Mathematical Method Hamiltonian System Numerical Scheme Error Growth Symplectic Scheme 
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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Donald J. Estep
    • 1
  • Andrew M. Stuart
    • 2
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlanta
  2. 2.Scientific Computing and Computational Mathematics Program, Division of Applied MechanicsStanford UniversityStanfordUSA

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