Scientific article

Variable time step integration with symplectic methods

ContributorsHairer, Ernst
Published inApplied numerical mathematics, vol. 25, no. 2-3, p. 219-227
Publication date1997

Symplectic methods for Hamiltonian systems are known to have favourable pro-per-ties concerning long-time integrations (no secular terms in the error of the energy integral, linear error growth in the angle variables instead of quadratic growth, correct qualitative behaviour) if they are applied with constant step sizes, while all of these properties are lost in a standard variable step size implementation. In this article we present a ``meta-algorithm'' which allows us to combine the use of variable steps with symplectic integrators, without destroying the above mentioned favourable properties. We theoretically justify the algorithm by a backward error analysis, and illustrate its performance by numerical experiments.

  • Hamiltonian systems
  • Symplectic integration
  • Variable step sizes
  • Backward error analysis
  • Kepler's problem
  • Verlet scheme
Citation (ISO format)
HAIRER, Ernst. Variable time step integration with symplectic methods. In: Applied numerical mathematics, 1997, vol. 25, n° 2-3, p. 219–227.
Main files (1)
Article (Published version)
  • PID : unige:12433
ISSN of the journal0168-9274

Technical informations

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