Geometric integration is the general term for a set of numerical algorithms for solving
differential equations that aim to reproduce qualitative features in the solution. These can be …

In Huang and Leimkuhler [SIAM J. Sci. Comput. 18 (1997) 239–256], a variable step-size,
semi-explicit variant of the explicit Störmer–Verlet method has been suggested for the time …

Abstract We consider Sundman and Poincaré transformations for the long-time numerical
integration of Hamiltonian systems whose evolution occurs at different time scales. The …

The scale invariant system of ordinary differential equations and the coupling of rescaling to
the invariance of the system were described. Self-similar solutions of the resulting equations …

Reversible and adaptive integration methods based on Kustaanheimo–Stiefel regularization
and modified Sundman transformations are applied to simulate general perturbed Kepler …

We consider adaptive geometric integrators for the numerical integration of Hamiltonian
systems with greatly varying time scales. A time regularization is considered using either the …

This article describes a gravitational N-body integration algorithm conserving linear and
angular momentum and time-reversal symmetry. Forces are dynamically partitioned based …

We show that adaptive time step** in particle accelerator simulation is an enhancement
for certain problems. The new algorithm has been implemented in the OPAL (Object …

We investigate the phase space structure and dynamics of a Hamiltonian isokinetic
thermostat, for which ergodic thermostat trajectories at fixed (zero) energy generate a …

We investigate the relation between the phase-space structures of Hamiltonian and non-
Hamiltonian deterministic thermostats. We show that phase-space structures governing …