ABSTRACT. Recently, a new family of integrators (Hamiltonian Boundary Value Methods) has been introduced, which is able to precisely conserve the energy function of polynomial Hamiltonian systems and to provide a practical conservation of the energy in the non-polynomial case. We settle the definition and the theory of such methods in a more general framework. Our aim is on the one hand to give account of their good behavior when applied to general 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 based upon the notion of extended collocation conditions and the definition of discrete line integral, and is carried out by looking at the limit of such family of methods as the number of the so called silent stages tends to infinity.

Hamiltonian Boundary Value Methods (Energy Preserving Discrete Line Integral Methods) / L.Brugnano; F.Iavernaro; D.Trigiante. - In: JOURNAL OF NUMERICAL ANALYSIS,INDUSTRIAL AND APPLIED MATHEMATICS. - ISSN 1790-8140. - STAMPA. - 5, 1-2:(2010), pp. 17-37.

Hamiltonian Boundary Value Methods (Energy Preserving Discrete Line Integral Methods)

BRUGNANO, LUIGI;TRIGIANTE, DONATO
2010

Abstract

ABSTRACT. Recently, a new family of integrators (Hamiltonian Boundary Value Methods) has been introduced, which is able to precisely conserve the energy function of polynomial Hamiltonian systems and to provide a practical conservation of the energy in the non-polynomial case. We settle the definition and the theory of such methods in a more general framework. Our aim is on the one hand to give account of their good behavior when applied to general 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 based upon the notion of extended collocation conditions and the definition of discrete line integral, and is carried out by looking at the limit of such family of methods as the number of the so called silent stages tends to infinity.
2010
5, 1-2
17
37
L.Brugnano; F.Iavernaro; D.Trigiante
File in questo prodotto:
File Dimensione Formato  
JNAIAM 5,1-2 (2010) 17-37.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 1.07 MB
Formato Adobe PDF
1.07 MB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/393590
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 240
  • ???jsp.display-item.citation.isi??? ND
social impact