For Hamiltonian systems, it is well established that symplectic methods have desirable long term stability properties, and methods within this class are now in widespread use for studying problems in lunar formation and solar system dynamics. Symplecticness can be a restrictive requirement in two particular situations: (i) systems with rapidly changing solutions, such as N-body problems with close approaches, and (ii) systems with components that evolve on a wide range of spatial and time scales. While less well established from a theoretical perspective, time-reversible methods appear to offer a practical, more flexible alternative to symplectic methods in some cases. In this talk I will describe some time-reversible schemes for model problems of types (i) and (ii).
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