Numerical Algorithms

, Volume 19, Issue 1–4, pp 55–71 | Cite as

Time-transformations for reversible variable stepsize integration

  • Stephen D. Bond
  • Benedict J. Leimkuhler


The development of a Sundman-type time-transformation for reversible variable stepsize integration of few-body problems is discussed. While a time-transformation based on minimum particle separation is suitable if the collisions only occur pairwise and isolated in time, the control of stepsize is typically much more difficult for a three-body close approach. Nonetheless, we find that a suitable choice of time-transformation based on particle separation can work quite well for certain types of three-body simulations, particularly those involving very steep repulsive walls. We confirm these observations using numerical examples from Lennard-Jones scattering.

adaptive Verlet method time-reversible methods adaptive timestepping variable stepsize methods N-body mechanical problems scattering Verlet 70-08 70F05 70F07 70F10 70H05 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Stephen D. Bond
    • 1
  • Benedict J. Leimkuhler
    • 1
  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

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