Title | Differential Equations in the Optimization of Catalytic Processes by Supercomputer Simulation |
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Authors | I. M. Gubaydullin^{1, 2}, K. F. Koledina^{1, 2}^{1}Institute of Petrochemistry and Catalysis of RAS ^{2}Ufa State Oil Technical University |

Annotation | The paper presents the results of a study of two industrially important processes with scientific groups from other regions. The general approaches and advan-tages of the groups are shown: 1) Bauman Moscow State Technical University -- polymerization, the process of formation of a high molecular weight substance (poly-mer) by repeated attachment of molecules of a low molecular weight substance (mono-mer) to active centers in a growing polymer molecule; 2) Keldysh Institute of Applied Mathematics RAS -- hydrocarbon fluid flow in a flow chemical reactor with a catalyst bed. As a result of the joint approach, the following have been developed: complex mathematical models that take into account the superrigidity of differential equations and include a quasi-hydrodynamic system of equations, supplemented by heat conduc-tion equations and convection-diffusion-reaction equations for fluid component concen-trations; technique for solving systems of differential equations based on grid methods; parallel algorithms for the implementation of numerical schemes based on MPI and OpenMP technologies; a set of programs for solving the selected class of problems; digital platform for conducting large-scale computational experiments. |

Keywords | mathematical modeling, polymerization, superstiff differential equations, hydrocarbon fluid, numerical methods |

Citation | Gubaydullin I. M., Koledina K. F. ''Differential Equations in the Optimization of Catalytic Processes by Supercomputer Simulation'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 54-60. Available at: https://conf.svmo.ru/files/2023/papers/paper07.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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