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">. 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.