G-symplectic second derivative general linear methods for Hamiltonian problems

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• 作者：M. Hosseini Nasab ^{m_hosseininasab@tabrizu.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; G. Hojjati ; ^{ghojjati@tabrizu.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; A. Abdi ^{a_abdi@tabrizu.ac.ir" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hamiltonian problems ; General linear methods ; Second derivative methods ; G-symplecticity ; Parasitism
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：486-498
• 全文大小：1334 K

文摘

It is our purpose to design second derivative general linear methods (SGLMs) for solving Hamiltonian problems. To do this, we explore G-symplectic SGLMs which preserve a generalization of quadratic invariants along the long-time integration. We find sufficient conditions on the coefficients matrices of the methods which ensure G-symplecticity and control parasitism. We construct such methods up to order class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716305003&_mathId=si10.gif&_user=111111111&_pii=S0377042716305003&_rdoc=1&_issn=03770427&md5=6baccbd1ec3a0d4171f4e9873d21bb34" title="Click to view the MathML source">4class="mathContainer hidden">class="mathCode">$4$. Numerical experiments of the constructed methods on the well-known Hamiltonian problems indicate ability of the methods in solving Hamiltonian problems over long-time integration.