I thought that instead of the great number of precepts of which logic is composed, I would
have enough with the four following ones, provided that I made a firm and unalterable …

Geometric integration is the numerical integration of a differential equation, while preserving
one or more of its' geometric'properties exactly, ie to within round-off error. Many of these …

We study analytically and experimentally certain symplectic and time-reversible N-body
integrators which employ a Kepler solver for each pair-wise interaction, including the …

We present a simple algorithm to switch between N-body time integrators in a reversible
way. We apply it to planetary systems undergoing arbitrarily close encounters and highly …

We present a new symplectic integrator designed for collisional gravitational N-body
problems which makes use of Kepler solvers. The integrator is also reversible and …

We present an efficient strategy for the numerical propagation of small Solar system objects
undergoing close encounters with massive bodies. The trajectory is split into several …

We apply one of the exactly symplectic integrators, which we call HB15, of Hernandez &
Bertschinger, along with the Kepler problem solver of Wisdom & Hernandez, to solve …

Symplectic integrators are the preferred method of solving conservative N-body problems in
cosmological, stellar cluster, and planetary system simulations because of their superior …

In this paper we discuss a two-dimensional adaptive grid method that is based on a tensor-
product approach. Adaptive grids are a commonly used tool for increasing the accuracy and …

A large gravitational (or classical atomic) N-body simulation typically includes fast binary
stars, planet-moon systems, or other tightly bound objects, demanding a small timestep and …