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Avtomatika i Telemekhanika, 2018, Issue 11, Pages 82–98
DOI: https://doi.org/10.31857/S000523100002745-3
(Mi at14642)
 

Control in Technical Systems

Solution of boundary problems with regard for inherent error on the basis of the Lagrange method

S. A. Nekrasov

South Russian State Polytechnical University, Novocherkassk, Russia
References:
Abstract: A two-sided method for calculation of the dynamic distributed-parameter systems with regard for the error of the reference data was proposed and substantiated using the variational principle of 'Lagrange. Calculation of the temperature fields with due regard for the phase transformations and errors in the parameters and characteristics was considered by way of an example. A relevant finite-difference method and computer programs for modeling the thermal physical processes of substance melting and crystallization in the case of imprecisely defined parameters and characteristics were developed. The direct Stefan problem was solved using a variant of the through “enthalpy” method. The conjugate problem was solved by smoothing the lumped heat capacity and other parameters and characteristics with a singularity of the delta-function type. Determination of the maximum/minimum of the temperature field, as well as the two-sided estimate of the solution gradient at the given point of the domain were considered as examples. In both cases, the specific power of the spatial data whose values lie within a certain band was regarded as given approximately. The present paper also cites examples of solving the similar stationary boundary problems. The results of work can be used in the practice of research and design in the areas of metallurgy, electrical apparatuses, criogenic engineering, and so on.
Keywords: two-sided method, boundary problem, inherent error, Stefan problem, temperature field, phase transition, enthalpy method.
Presented by the member of Editorial Board: A. G. Kushner

Received: 16.01.2017
English version:
Automation and Remote Control, 2018, Volume 79, Issue 11, Pages 2018–2032
DOI: https://doi.org/10.1134/S0005117918110061
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. A. Nekrasov, “Solution of boundary problems with regard for inherent error on the basis of the Lagrange method”, Avtomat. i Telemekh., 2018, no. 11, 82–98; Autom. Remote Control, 79:11 (2018), 2018–2032
Citation in format AMSBIB
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\paper Solution of boundary problems with regard for inherent error on the basis of the Lagrange method
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\pages 82--98
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\jour Autom. Remote Control
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\issue 11
\pages 2018--2032
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