Year: 2007
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 6 : pp. 690–696
Abstract
We prove that any linear multi-step method Gτ1 of the form m∑k=0αkZk=τm∑k=0βkJ−1∇H(Zk) with odd order u (u≥3) cannot be conjugate to a symplectic method Gτ2 of order w (w≥u) via any generalized linear multi-step method Gτ3 of the form m∑k=0αkZk=τm∑k=0βkJ−1∇H(m∑l=0γklZl). We also give a necessary condition for this kind of generalized linear multi-step methods to be conjugate-symplectic. We also demonstrate that these results can be easily extended to the case when Gτ3 is a more general operator.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-JCM-8722
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 6 : pp. 690–696
Published online: 2007-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 7
Keywords: Linear multi-step method Generalized linear multi-step method Step-transition operator Infinitesimally symplectic Conjugate-symplectic.