Integration of Coulombic N-body problems involving close approaches is a standard problem in astrophysics and is also encountered in certain quasi-classical approaches to atomic problems. Stable integration requires the use of coupled time and coordinate transformations (Kustaanheimo-Stiefel regularization). In this talk, the author will show that the KS framework can be combined with an additional time-transformation and a special integration method to yield a symmetry-preserving integrator. For systems dominated by two-body (as opposed to three-body, or more) close approaches, an argument can be made that preservation of symmetry leads to improved numerical behavior.
Examples such as He+e- scattering and perturbed Kepler problems illustrate the dramatic improvements obtainable by the adaptive-reversible schemes.