The inverse problem of restoring the parameters of a mathematical model with a given data error
Abstract
This work is devoted to inverse problems of restoring the parameters of a mathematical model with a given error in the initial data. The purpose of the work is to find an approximation to the parameters of the mathematical model. A mathematical model in the form of a system of ordinary differential equations is considered. An inverse problem has been formed: according to the measured data of the properties or behavior of the object under study, i.e. according to the given values of the unknown functions of the mathematical model, determine the values of its parameters. To solve the inverse problem, a technique constructed using the Tikhonov regularization method was used. The generalized residual method was used to select the regularization parameter. As a numerical example, a mathematical model is considered that describes the kinetics of the oil refining process. With a given error of the initial data, the inverse problem of restoring the mathematical model is solved. As a result of the calculations, approximations to the parameters of the considered mathematical model were found. The results of our work consist not only in restoring the parameters of the mathematical model, but also have the following practical significance. With the found approximate parameters, it is possible to predict a change in the properties or behavior of the object under study over time, for example, a change in the concentration of substances and products during oil refining.
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