Kinetic equations describing nucleation on active centers are solved numerically to determine the number of supercritical nuclei, nucleation rate, and the number density of nuclei for formation both of droplets from vapor and also crystalline phase from vapor, solution, and melt. Our approach follows standard nucleation model, when the exhaustion of active centers is taken into account via the boundary condition, and thus no additional equation (expressing exhaustion of active centers) is needed. Moreover, we have included into our model lowering of supersaturation of a mother phase as a consequence of the phase transition process within a confined volume. It is shown that the standard model of nucleation on active centers (Avrami approach) gives faster exhaustion of active centers as compared with our model in all systems under consideration. Nucleation rate (in difference to standard approach based on Avrami model) is equal to the time derivative of the total number of nuclei and reaches some maximum with time. At lower nucleation barrier (corresponding to higher initial supersaturation or lower wetting angle of nucleus on the surface of active center) the exhaustion of active centers is faster. Decrease in supersaturation of the mother phase is faster at higher number of active centers.