BIT Numerical Mathematics

, Volume 39, Issue 1, pp 25–33 | Cite as

Asymptotic Error Analysis of the Adaptive Verlet Method

  • Stéphane Cirilli
  • Ernst Hairer
  • Benedict Leimkuhler


The Adaptive Verlet method and variants are time-reversible schemes for treating Hamiltonian systems subject to a Sundman time transformation. These methods have been observed in computer experiments to exhibit superior numerical stability when implemented in a counterintuitive “reciprocal” formulation. Here we give a theoretical explanation of this behavior by examining the leading terms of the modified equation (backward error analysis) and those of the asymptotic error expansion. With this insight we are able to improve the algorithm by simply correcting the starting stepsize.

Adaptive Verlet method time-reversible variable stepsizes Hamiltonian systems Sundman time-transformations backward error analysis asymptotic expansions 


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Copyright information

© Swets & Zeitlinger 1999

Authors and Affiliations

  • Stéphane Cirilli
    • 1
  • Ernst Hairer
    • 1
  • Benedict Leimkuhler
    • 2
  1. 1.Section de mathématiquesUniversité de GenèveGenève 24Switzerland, email
  2. 2.Department of Mathematics, 405 Snow HallUniversity of KansasLawrenceUSA

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