Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A generalization to variable stepsizes of Sto¨rmer methods for second-order differential equations
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
Variable time step integration with symplectic methods
Applied Numerical Mathematics - Special issue on time integration
Variable step implementation of geometric integrators
Applied Numerical Mathematics
Reversible adaptive regularization methods for atomic N-body problems in applied fields
proceedings of the on Numerical analysis of hamiltonian differential equations
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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.