Abstract

In this paper, we provide a simple framework to derive and analyse a class of one-step methods that may be conceived as a generalization of the class of Gauss methods. The framework consists in coupling two simple tools: firstly a local Fourier expansion of the continuous problem is truncated after a finite number of terms and secondly the coefficients of the expansion are computed by a suitable quadrature formula. Different choices of the basis lead to different classes of methods, even though we shall here consider only the case of an orthonormal polynomial basis, from which a large subclass of Runge-Kutta methods can be derived. The obtained results are then applied to prove, in a simplified way, the order and stability properties of Hamiltonian BVMs (HBVMs), a recently introduced class of energy preserving methods for canonical Hamiltonian systems (see [2] and references therein). A few numerical tests are also included, in order to confirm the effectiveness of the methods resulting from our analysis.

Autore Pugliese

• Iavernaro Felice

Tutti gli autori

• IAVERNARO F.

Titolo volume/Rivista

Non Disponibile

Anno di pubblicazione

2012

ISSN

0096-3003

ISBN

Non Disponibile

Numero di citazioni Wos

49

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

54

Ultimo Aggiornamento Citazioni

Non Disponibile

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile