EXPANSIONS OF STEP-TRANSITION OPERATORS OF MULTI-STEP METHODS AND ORDER BARRIERS FOR DAHLQUIST PAIRS  

作　　者：Quan-dong Feng Yi-fa Tang 

机构地区：[1]LSEC, ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China [2]Graduate School of the Chinese Academy of Sciences, Beijing 100080, China

出　　处：《Journal of Computational Mathematics》2006年第1期45-58,共14页计算数学（英文）

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.

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.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.

关 键 词：Linear Multi-Step Method Step-Transition Operator B-SERIES Dahlquist（Conjugate） pair SYMPLECTICITY 

分 类 号：O24[理学—计算数学]