Abstract

It is known that symplectic algorithms do not necessarily conserve energy even for the harmonic oscillator. However, for separable Hamiltonian systems, splitting and composition schemes have the advantage to be explicit and can be constructed to preserve energy. In this paper we describe and test an integrator built on a one-parameter family of symplectic symmetric splitting methods, where the parameter is chosen at each time step so as to minimize the energy error. For second-degree polynomial Hamiltonian functions as the one describing the linear oscillator, we build up second and fourth order symmetric methods which are symplectic, energy-preserving and explicit. For non-linear examples, it is possible to construct schemes with minimum error on energy conservation. The methods are semi-explicit in the sense that they require, as additional computational effort, the search for a zero of a scalar function with respect to a scalar variable. Therefore, our approach may represent an effective alternative to energy-preserving implicit methods whenever multi-dimensional problems are dealt with as is the case of many applications of interest.

Autore Pugliese

• Marangi Carmela , Diele Fasma

Tutti gli autori

• B. Pace ; F. Diele ; C. Marangi

Titolo volume/Rivista

Mathematics and computers in simulation

Anno di pubblicazione

2015

ISSN

0378-4754

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

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Numero di citazioni Scopus

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Ultimo Aggiornamento Citazioni

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Settori ERC

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Codici ASJC

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