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The work contains a mathematical description of diene polymerization with a neodym-based Ziegler-Natta catalysts. The resulting system of differential equations was reduced from infinite to finite by the method of moments. For this, the basis of nonlinear parametric functions was searched with a method allowing obtain expressions that reflect the kinetics of the polymerization process. The obtained basis of two functions enables us to construct a surface containing local regions of the minimum of the objective function which define the starting points for search of optimum kinetic constant values.

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This article presents a 16-lump model of catalytic cracking of vacuum gasoil, which allows to take into account the quantity and quality of the main products of the process: gasoline, propane-propylene and butane-butylene fractions; and by-products of the process: light and heavy catalytic gasoil. To solve the direct problem of solving a system of differential equations, the Runge-Kutta method of order 4 is used, to solve the inverse problem of choosing the constants of the rate of chemical transformations, the method of direct search for minimizing the function of the sum of deviations of calculated values from experimental ones is applied. Thus, the reaction rate constants were chosen for the developed model.