The Lack of Continuity and the Role of Infinite and Infnitesimal in Numerical Methods for ODEs: the Case of Symplecticity

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Abstract

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.

Autore Pugliese

Tutti gli autori

  • IAVERNARO F.

Titolo volume/Rivista

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Anno di pubblicazione

2012

ISSN

0096-3003

ISBN

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Numero di citazioni Wos

Nessuna citazione

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Numero di citazioni Scopus

32

Ultimo Aggiornamento Citazioni

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Settori ERC

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Codici ASJC

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