Palindromic 3-stage splitting integrators, a roadmap

The implementation of multi-stage splitting integrators is essentially the same as the implementation of the familiar Strang/Verlet method. Therefore multi-stage formulas may be easily incorporated into software that now uses the Strang/Verlet integrator. We study in detail the two-parameter family of palindromic, three-stage splitting formulas and identify choices of parameters that may outperform the Strang/Verlet method. One of these choices leads to a method of effective order four suitable to integrate in time some partial differential equations. Other choices may be seen as perturbations of the Strang method that increase efficiency in molecular dynamics simulations and in Hybrid Monte Carlo sampling.Comment: 20 pages, 8 figures, 2 table

The Infrared-X-ray continuum correlation in Active Galactic Nuclei

The correlation between the soft X-ray and near infrared emission from AGN is analysed using composite models by the code SUMA. We find new evidences for differences in ranges of parameters which characterize the NLR of Seyfert galaxies and LINERs. Results obtained by modelling the Einstein and the ROSAT samples of galaxies are in full agreement. In order to fit the infrared and X-ray continua, an eta factor is defined, which accounts for the emitting area of the cloud. If the infrared emission is due to bremsstrahlung and comes from the same cloud producing the soft X-rays, the eta values obtained from both emissions must be the same. Therefore, if eta_IR < eta_soft-X there must be a strong contribution of soft X-rays from the active centre. From the eta values we expect to identify the objects that could present strong variability. \Comment: 11 pages,13 figures, in press in MNRAS. in press in MNRA