Abstract

Recently, the class of Hamiltonian Boundary Value Methods (HBVMs) has been introduced with the aim of preserving the energy associated with polynomial Hamiltonian systems (and, more in general, with all suitably regular Hamiltonian systems). However, many interesting problems admit other invariants besides the Hamiltonian function. It would be therefore useful to have methods able to preserve any number of independent invariants. This goal is achieved by generalizing the line-integral approach which HBVMs rely on, thus obtaining a number of generalizations which we collectively name Line Integral Methods. In fact, it turns out that this approach is quite general, so that it can be applied to any numerical method whose discrete solution can be suitably associated with a polynomial, such as a collocation method, as well as to any conservative problem. In particular, a completely conservative variant of both HBVMs and Gauss collocation methods is presented. Numerical experiments confirm the effectiveness of the proposed methods.

Autore Pugliese

• Iavernaro Felice

Tutti gli autori

• IAVERNARO F.

Titolo volume/Rivista

Non Disponibile

Anno di pubblicazione

2012

ISSN

0377-0427

ISBN

Non Disponibile

Numero di citazioni Wos

24

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

26

Ultimo Aggiornamento Citazioni

Non Disponibile

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile