Jc. Chiou et Sd. Wu, OPEN NEWTON-COTES DIFFERENTIAL METHODS AS MULTILAYER SYMPLECTIC INTEGRATORS, The Journal of chemical physics, 107(17), 1997, pp. 6894-6898
Open Newton-Cotes differential methods that possess the characteristic
s of multilayer symplectic structures are shown in this paper. In nume
rical simulation, volume-preservation plays an important role in solvi
ng the Hamiltonian system. In this regard, developing a numerical inte
grator that preserves the volume in the phase space of a Hamiltonian s
ystem is a great challenge to the researchers in this field. Symplecti
c integrators were proven to be good candidates for volume-preserving
integrators (VPIs) in the past ten years. Several one-step (single-sta
ge or multistages) symplectic integrators have been developed based on
the symplectic geometric theory. However, multistep VPIs have seldom
been investigated by other researchers for the lack of an advanced the
ory. Recently, Zhu et al. converted open Newton-Cotes differential met
hods into a multilayer symplectic structure so that multistep VPIs of
a Hamiltonian system are obtained. Mainly, their work has concentrated
on the issue of achieving both the accuracy and efficiency by solving
the quantum systems. But, there exist some unclear aspects in derivin
g this result in their paper. In this regard, we resolve their problem
and provide a different aspect in connecting the relationship between
open Newton-Cotes differential methods and symplectic integrators. A
numerical example has been carried out to show the effectiveness of th
e present differential method. (C) 1997 American Institute of Physics.
[S0021-9606(97)02234-4].