Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Khromov A. A., Khromova G. V. The Solution of the Problem of Determining the Density of Heat Sources in a Rod. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 3, pp. 309-314. DOI: 10.18500/1816-9791-2015-15-3-309-314, EDN: UKIVFZ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
11.09.2015
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Russian
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UKIVFZ

The Solution of the Problem of Determining the Density of Heat Sources in a Rod

Autors: 
Khromov Alexander Avgustovich, Saratov State University
Khromova Galina Vladimirovna, Saratov State University
Abstract: 

We give a solution of a problem of determining the density of heat sources in the bav, which is set to a fixed temperature, if the temperature is given approximately. Mathematically it is the problem of finding uniform approximations to the right-hand side of the ordinary differential equation when uniform approximations to the solution and values of error are known. First using the so-called discontinuous Steklov operator we construct families of operators which give stable uniform approximations to a function and its first and second derivatives, and then with their help we propose the method of solving the formulated problem. For a certain class of solutions error estimations are given.

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Received: 
17.04.2015
Accepted: 
26.08.2015
Published: 
30.09.2015