In this paper we are concerned with the analysis of a class of geometric integrators, at first devised in Brugnano et al. (2010) and Brugnano et al. (2012), which can be regarded as an energy-conserving variant of Gauss collocation methods. With these latter they share the property of conserving quadratic first integrals but, in addition, they also conserve the Hamiltonian function itself. We here reformulate the methods in a more convenient way, and propose a more refined analysis than that given in Brugnano et al. (2012) also providing, as a by-product, a practical procedure for their implementation. A thorough comparison with the original Gauss methods is carried out by means of a few numerical tests solving Hamiltonian and Poisson problems.
Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods
Brugnano, Luigi;Iavernaro, Felice
2018-01-01
Abstract
In this paper we are concerned with the analysis of a class of geometric integrators, at first devised in Brugnano et al. (2010) and Brugnano et al. (2012), which can be regarded as an energy-conserving variant of Gauss collocation methods. With these latter they share the property of conserving quadratic first integrals but, in addition, they also conserve the Hamiltonian function itself. We here reformulate the methods in a more convenient way, and propose a more refined analysis than that given in Brugnano et al. (2012) also providing, as a by-product, a practical procedure for their implementation. A thorough comparison with the original Gauss methods is carried out by means of a few numerical tests solving Hamiltonian and Poisson problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
