Next: Imaging by an Optimizing Method . ... A big advantage of this numerical integrator is its stability: the error in the semi-major axis and the eccentricity depends only on the step size and does not grow with an increasing number of time steps. ... As the integration time increases, the numerical results become more contaminated by various errors. ... A new symplectic integrator produces no secular truncation errors in the actions of a Hamiltonian system. ...