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7A method for inverting a finite-difference scheme is developed and implemented, a gradient method for
solving the inverse problem is implemented, and a gradient formula is obtained. A comparative analysis of the
developed methods is carried out. The methods are tested on experimental data.
The work was carried out with the financial support of the Russian Foundation for Basic Research (project code
20-51-54004).
References
1. Belonosov A., Shishlenin M., Klyuchinskiy D. A comparative analysis of numerical methods of solving the continua-
tion problem for 1D parabolic equation with the data given on the part of the boundary // Advances in Computational
Mathematics. 2019. V. 45, No 2. P. 735�755.
Regularization of inclusions of differential equations solutions based on the kinematics of a vector field
in problems of stability of a set of trajectories
A. N. Rogalev
Institute of Computational Modelling SB RAS, Krasnoyarsk
Email: rogalyov@icm.krasn.ru
DOI 10.24412/cl-35065-2021-1-02-08
In the papers of specialists on stability problems, it is proposed to investigate stability problems for a set
of trajectories of nonlinear dynamics under the influence of arbitrary perturbing influences [1]. In this report,
to estimate the stability of the sets of solutions, the boundaries of the sets of solutions will be efficiently and
accurately computed applying symbolic formulas for solutions of ordinary differential equations [2] and evalu-
ating the parameters of the kinematics of the vector field. The parameters of the vector field kinematics per-
form regularization, which eliminates the excessive growth of the boundaries of the inclusions. The examples
show the advantages of this approach to solving stability problems for a set of trajectories.
This work was carried out within the framework of the state assignment of the Federal Research Center of the KSC
SB RAS, project No. 0287-2021-0002.
References
1. Martynyuk A. Stability of a Set of Trajectories of Nonlinear Dynamics // Doklady Akademii Nauk. 2007. V. 414,
No. 3. P. 299-303.
2. Rogalev A.N., Rogalev A.A., Feodorova N.A. Numerical Computations of the Safe Boundaries of Complex Technical
Systems and Practical Stability// J. of Physics: Conference Series 1399 (2019) 033112. doi:10.1088/1742-6596/1399/3/
033112.
Regularization of the global error estimation for numerical solutions of differential equations based
on tracking approximate trajectories
A. N. Rogalev
Institute of Computational Modelling SB RAS, Krasnoyarsk
Email: rogalyov@icm.krasn.ru
DOI 10.24412/cl-35065-2021-1-02-09
The main idea of the regularization of the global error estimate is that new variables or new relations are
introduced that make it possible to reduce (or even eliminate) the influence of the Lyapunov instability on the
bounds of the numerical solutions and to refine these estimates. Such a regularization was performed in sev-
eral works of the author, for example, in [1]. In this report, it is proposed to consider the perturbed system as
a modified model based on pseudo-trajectories (approximate) trajectories, the effect of numerical errors on
the pseudo-trajectories, including round-off errors, leads to the actual study of the trajectory with some ap-
proximation. The report proposes to use pseudo-trajectories to consider the data space as a space of problems
and to estimate the relationship between a defect, local and global errors of numerical solutions. Examples of
numerical estimates of the global error are given.
This work was carried out within the framework of the state assignment of the Federal Research Center of the KSC
SB RAS, project No. 0287-2021-0002.
References
1. Rogalev A. N., Feodorova N.A. Regularization of algorithms for estimation of errors of differential equations
approximate solutions // J. of Physics: Conference Series 1715 (2021) 012044 doi:10.1088/1742-6596/1715/1/012044.
Kinetic modeling of propane pyrolysis: parameters identifiability and estimation
L. F. Safiullina1, I. M. Gubaydullin2
1Bashkir State University, Ufa
2Institute of Petrochemistry and Catalysis UFRC RAS
Email: SafiullinaLF@gmail.com
DOI 10.24412/cl-35065-2021-1-02-10
One of heavy olefins upgrading processes is pyrolysis. As it is a complex process involving many chemical
reactions, the mathematical model of pyrolysis process often has more kinetic parameters than can be esti-
mated from the data. In this article, a kinetic model for propane pyrolysis processing is proposed. It is proved
that the model is practically identifiable. Practical identifiability analysis is based on simulated model outputs
and their sensitivities with respect to parameters [1, 2]. As a result of the analysis of identifiability, the least
and most sensitive parameters to measurements were identified. The minimization problem was solved
through the genetic algorithm method that is widely applied for stochastic global optimization. It has been
demonstrated that kinetic model describes the experimental data of the observed substances of the reaction.
The reported study was funded by RFBR, project number 19-37-60003.
References
1. Yao K.Z., Shaw B.M., Kou B., McAuley K.B., Bacon D.W. Modeling ethylene/butene copoly-merization with
multi-site catalysts: parameter estimability and experimental design. Polymer Reaction Engineer. 2003.11(3). 563-588.
2. Safiullina L.F., Gubaydullin I.M. Numerical analysis of parameter identifiability for a mathematical model of a
chemical reaction. International J. of Engineering Systems Modelling and Simulation. 2020. 11(4). 207-213.
Multiplicative control problems for semilinear reaction-diffusion-convection equation
Zh. Yu. Saritskaia1,2, R. V. Brizitskii1,2
1Institute of Applied Mathematics FEB RAS
2Far Eastern Federal University, Vladivostok
Email: zhsar@icloud.com, mlnwizard@mail.ru
DOI 10.24412/cl-35065-2021-1-02-11
The interest in the study of boundary value and control problems for linear as well as for nonlinear models
for mass and heat transfer does not fade over sufficiently long time (see [1, 2] and References in there). In this
paper, we consider multiplicative control problems for the semilinear reaction-diffusion-convection equation.
The coefficients in both the equation and the boundary condition of the model under consideration depend on
the solution of the boundary value problem (see [2]). The diffusion coefficient plays a role of a multiplicative
