EXPANSIONS OF STEP-TRANSITION OPERATORS OF MULTI-STEP METHODS AND ORDER BARRIERS FOR DAHLQUIST PAIRS
EXPANSIONS OF STEP-TRANSITION OPERATORS OF MULTI-STEP METHODS AND ORDER BARRIERS FOR DAHLQUIST PAIRS作者机构：LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Graduate School of the Chinese Academy of Sciences Beijing 100080 China
出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)
年 卷 期：2006年第24卷第1期
页 面：45-58页
核心收录：
学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学]
基 金：This research is supported by the Informatization Construction of Knowledge Innovation Projects of the Chinese Academy of Sciences "Supercomputing Environment Construction and Application" (INF105-SCE) and by a grant (No. 10471145) from National Natural Science Foundation of China
主 题：Linear Multi-Step Method Step-Transition Operator B-series Dahlquist(Conjugate) pair Symplecticity
摘 要：Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained by the second author in a former paper）. We prove that in the conjugate relation G3^λτ o G1^τ =G2^τ o G3^λτ with G1 being an LMSM,（1） theorder of G2 can not be higher than that of G1; （2） if G3 is also an LMSM and G2 is a symplectic B-series, then the orders of G1, G2 and G3 must be 2, 2 and 1 respectively.
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