Hamiltonian Boundary Value Methods ( Energy Preserving Discrete Line Integral Methods ) 1 2
Hamiltonian Boundary Value Methods ( Energy Preserving Discrete Line Integral Methods ) 1 2
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DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
L. Brugnano;F. Iavernaro;D. Trigiante
中科院分区：
文献类型：
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作者：
L. Brugnano;F. Iavernaro;D. Trigiante
翻译后摘要：最近，一个新的家庭的积分（哈密顿边值方法）已被引入，这是能够精确地保存多项式哈密顿系统的能量函数，并提供apractical的非多项式情况下的能量守恒。我们在一个更一般的框架内解决了这种方法的定义和理论。我们的目的是一方面考虑到他们的良好行为时，适用于一般的哈密顿系统，另一方面，找出什么是最佳的公式，在选择的多项式基础和节点的分布。这种分析是基于扩展配置条件的概念和离散线积分的定义，并通过考察这类方法在所谓的级数趋于无穷大时的极限来进行的。
Abstract:Recently, a new family of integrators (Hamiltonian Boundary Value Methods ) ha been introduced, which is able to precisely conserve the energy function of poly nomial Hamiltonian systems and to provide apractical conservation of the energy in the non-polynomial case. We settle the definition and the theory of such methods in a more general fra mework. Our aim is on the one hand to give account of their good behavior when applied to gene ral Hamiltonian systems and, on the other hand, to find out what are the optimal formulae, in relation to the choice of the polynomial basis and of the distribution of the nodes. Such analysis is base d upon the notion of extended collocation conditions and the definition ofdiscrete line integral , and is carried out by looking at the limit of such family of methods as the number of the so called sil nt stagestends to infinity.