Explicit symplectic algorithms for time-transformed Hamiltonians
The authors discuss a special time transformation, such that applied to a separated Hamiltonian, the transformed Hamiltonian is again separated and thus permits the use of explicit symplectic integrators. It is shown that the application of leapfrog algorithm to the time-transformed two-body motion yields the exact Keplerian ellipse; errors appear only in the integration of the time variable. After a discussion of \(N\)-body systems and the use of higher-order methods, the authors present results of some numerical experiments. They show that even collision orbits can be computed without catastrophic errors.
scientific article; zbMATH DE number 1442301