Multistep Methods for Conservative Problems
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We discuss the use of linear multistep methods for the solution of conservative (in particular Hamiltonian) problems. Despite the lack of good results concerning their behaviour, linear multistep methods have been satisfactorily used by researchers in applicative fields. We try to elucidate the requirements that a linear multistep method should fulfill in order to be suitable for the integration of such problems, relating our analysis to their use as boundary value methods. We collect a number of results obtained for the linear autonomous case and also consider some numerical tests on the Kepler problem.
Mathematics Subject Classification (2000).Primary 65P10 Secondary 65L05 65L10
Keywords.Linear multistep methods Hamiltonian systems simplecticity boundary value methods
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