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

• 来源期刊: 计算数学（英文版）
• 关键词: Linear Multi-Step Method Step-Transition Operator B-series Dahlquist (Conjugate) pair Symplecticity
• 年，卷（期）: 2006,（1）
• 页码范围: 45-58
• 页数: 14页
• 语种: 英文

摘要

Using least parameters, we expand the step-transition operator of any linear multi-step method (LMSM) up to O(τs+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 Gλ3τoGτ1T = Gτ2oGλτ3 with G1 being an LMSM, (1) the order 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.