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Accurate long-term integration of dynamical systems. (English) Zbl 0837.65071
Properties concerning the global error of the integration performed over a very long time of a system of differential equations by symplectic or symmetric methods are studied. It is shown that the error growth – for problems with periodic solution and for integrable systems using symplectic or symmetric methods – is only linear in \(t_n\), compared to a quadratic error growth in the general case. A variable stepsize implementation for symmetric collocation methods is also explained.

MSC:
65L05 Numerical methods for initial value problems
65L70 Error bounds for numerical methods for ordinary differential equations
37-XX Dynamical systems and ergodic theory
34C25 Periodic solutions to ordinary differential equations
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