Variable step implementation of geometric integrators Original Research Article

We compare experimentally several techniques for combining geometric integrators with variable time steps. In particular, we study modifications of the Verlet method due to Leimkuhler and a technique for symplectic integration based on Poincaré transformations suggested by Hairer and Reich independently. We conclude that it is feasible to develop symplectic 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.