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Stephen D. Bond


Stephen D. Bond and Benedict J. Leimkuhler, Time-Transformations for Reversible Variable Stepsize Integration, Numerical Algorithms 19 (1998) 55-71.


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.

Full Text:

DOI: 10.1023/A:1019127111709


Time-Transformations for Reversible Variable Stepsize Integration (336K, PDF)

  author  = {Stephen D. Bond and Benedict J. Leimkuhler},
  title   = {Time-Transformations for Reversible Variable Stepsize
  journal = {Numerical Algorithms},
  volume  = 19,
  year    = 1998,
  pages   = {55--71},
  doi     = {10.1023/A:1019127111709}

Stephen Bond