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It has previously been shown that varying the numerical timestep during asymplectic orbital integration leads to a random walk in energy and angularmomentum, destroying the phase space-conserving property of symplecticintegrators. Here we show that when altering the timestep symplectic correctorscan be used to reduce this error to a negligible level. Furthermore, thesecorrectors can also be employed to avoid a large error introduction whenchanging the Hamiltonian's partitioning. We have constructed a numericalintegrator using this technique that is nearly as accurate as widely usedfixed-step routines. In addition, our algorithm is drastically faster forintegrations of highly eccentricitic, large semimajor axis orbits, such asthose found in the Oort Cloud.

Decreasing Computing Time with Symplectic Correctors in Adaptive Timestepping Routines