کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4630704 | 1340605 | 2012 | 8 صفحه PDF | دانلود رایگان |
When numerically integrating canonical Hamiltonian systems, the long-term conservation of some of its invariants, for example the Hamiltonian function itself, assumes a central role. The classical approach to this problem has led to the definition of symplectic methods, among which we mention Gauss–Legendre collocation formulae. Indeed, in the continuous setting, energy conservation is derived from symplecticity via an infinite number of infinitesimal contact transformations. However, this infinite process cannot be directly transferred to the discrete setting. By following a different approach, in this paper we describe a sequence of methods, sharing the same essential spectrum (and, then, the same essential properties), which are energy preserving starting from a certain element of the sequence on, i.e., after a finite number of steps.
Journal: Applied Mathematics and Computation - Volume 218, Issue 16, 15 April 2012, Pages 8056–8063