It is well known the great deal of advantages of integrating reversible systems with symmetric methods. The correct qualitative behaviour is imitated, which leads also to quantitative advantageous properties with respect to the errors and their growth with time. More particularly, fixed stepsize symmetric linear multistep methods especially designed for second order differential equations can integrate very efficiently periodic or quasiperiodic orbits till long times. A study will be given on what happens when variable stepsizes are considered so as to deal with highly eccentric orbits.
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