A note on symplecticity of step-transition mappings for multi-step methods

Authors:
Gui-Dong Dai;Yi-Fa Tang
Affiliations:
LSEC, ICMSEC, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, P.R. China and Graduate School of the Chinese Academy of Sciences, Beijing, P.R. China;LSEC, ICMSEC, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, P.R. China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

We prove that for a linear multi-step method Σk=0mαk Zk =τ Σk=0mβk f(Zk), even though the mappings Z0 → Z1,...,Zm-2 → Zm-1 are chosen to be symplectic, Zm-1 → Zm will be non-symplectic. Similarly, there is an interesting result for a sort of general linear methods.