Analytical and numerical models of the description of proto-planet disk of the Sun at an initial stage of it evolution are considered. The solutions for proto-planet disk of the Sun and solution for planetary gas rings of proto-planet disk are found. The calculations of stationary state of planetary rings of a proto-planet disk and evolution of a planetary ring being in non-stationary state are executed. The results of analytical and numerical calculations, their analysis and comparison are given. The model of formation of a planetary system of the Sun is offered.

Mathematical modelling in actual problems of science and technics