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.
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