VARIABLE STEP IMPLEMENTATION OF GEOMETRIC INTEGRATORS

We compare experimentally several techniques for combining geometric i ntegrators with variable time steps. In particular, we study modificat ions of the Verlet method due to Leimkuhler and a technique for symple ctic integration based on Poincare transformations suggested by Hairer and Reich independently. We conclude that it is feasible to develop s ymplectic variable step size codes that, for Hamiltonian problems, are competitive with standard software. We also analyze the error growth of the new algorithms when integrating periodic orbits. (C) 1998 Elsev ier Science B.V. and IMACS. All rights reserved.