The Observer-New Method for Numerical Integration of Differential Equations in the Presence of First Integrals
In celestial mechanics and dynamical astronomy the numerical integration of differential equations is one of the most popular and practical method of a study of dynamical systems. Recently a quite big progress was made in developing new more reliable methods of integration of differential equations. For Hamiltonian system different kinds of symplectic integrators were found (see Sanz-Serna 1992 for overview) and for more general Lie-Poisson system the Lie-Poisson integrators were developed (see Ge and Marsden 1988, Channell and Scovel 1991). This kind of integrators are especially important in celestial mechanics where most of dynamical systems are Hamiltonian. For general system of differential equations it seems that most promising recent achievements were done in the analytical continuations methods (see Gofen 1992 and references cited there).
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