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The symplecticity of multi-step methods

✍ Scribed by Yi-Fa Tang

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
303 KB
Volume
25
Category
Article
ISSN
0898-1221

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✦ Synopsis

For any linear multi-step scheme, Feng Kang defines the step-transition operator characterizing it and defines the symplectlcity of the method for Hamiltonian systems through the operator. In this paper, the author gets a valuable expression of the step-transitlon operator (Lemma 1, Section 2) and proves a conjecture due to Feng--any linear multi-step scheme is non-symplectic (Theorem 1, Section 3). Similarly, an interesting result (in Theorem 2, Section 3) for a sort of generalized multi-step schemes is obtained. The results indicate that some novel approach is needed for the construction of symplectic multi-step methods.

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