An implementation of geometric integration within Matlab

Geometric integrators allow preservation of specific geometric properties of the exact flow of differential equation systems, such as energy, phase-space volume, and time-reversal symmetry, and are particularly reliable for long-run integration. In this study, variable step size composition methods and Gauss methods are implemented in Matlab library integrators, and are tested with several representative problems, including the Kepler problem, the outer solar system and a conservative Lotka–Volterra system. Variable step size integrators often perform better than their fixed step size counterparts and the numerical results show excellent long time preservation of the Hamiltonian in these examples.