Numerical evolutionary models of planetary nebulae

The evolutionary sequences of planetary nebulae (PN) numerical models were constructed from the moment of PN envelope detachment up to its dissipation. Spherical symmetry was suggested. Dynamical influences of radiation pressure on dust, of ionization front and fast stellar wind were included in the models. Spectra of outgoing radiation were calculated for infrared and radio frequency range. The models give a general outline of evolution of spectral and dynamical PN parameters. Comparison with observed spectra of NGC 7027 and the observed ''radius-expansion velocity'' dependence shows that the models can be of use also for analysis of observations