The mathematical model of the first-order phase transition due to fluctuation of thermodynamical parameters presented as system of equations of mathematical physics in partial derivatives of the Kolmogorov-Feller and Einstein-Smolukhovskyi and stochastic differential equations of Ito-Stratonovich. Computer simulation study of the nonlinear stage of nucleation can be used in the powders synthesis and thin films of silicon carbide. Model processes of condensation and crystallization are presented as superposition of Wiener random processes such as stochastic diffusion in phase space cluster sizes of nuclei and spatial their Brownian motion on the surface and in the volume of the substrate. The computations using the effective algorithms for stochastic differential equations with nonlinear coefficients are presented by kinetic functions of distribution clusters of nuclei from size and spatial coordinates for the conditions of numerical experiments, which meet the definition of the 'open' physical system.

Mathematical modelling in actual problems of science and technics