NON-EXISTENCE OF CONJUGATE-SYMPLECTIC MULTI-STEP METHODS OF ODD ORDER

• 来源期刊: 计算数学（英文版）
• 关键词: Linear multi-step method Generalized linear multi-step method Step-transition operator Infinitesimally symplectic Conjugate-symplectic
• 年，卷（期）: 2007,（6）
• 页码范围: 690-696
• 页数: 7页
• 语种: 英文

摘要

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.