Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

For citation:

Khromov A. A. The Solution of a Certain Inverse Problem. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 2, pp. 180-183. DOI: 10.18500/1816-9791-2016-16-2-180-183, EDN: WCNQKV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.06.2016
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Language: 
Russian
Heading: 
Mathematics
UDC: 
519.642.8
DOI: 
10.18500/1816-9791-2016-16-2-180-183
EDN: 
WCNQKV

The Solution of a Certain Inverse Problem

Autors: 
Khromov Alexander Avgustovich, Saratov State University
Abstract: 

The solution is given for the problem of findinging uniform approximations of a the right-hand side of a general linear ordinary differential equation in the case when approximations of the exact solution are known. The constructed method has a simple structure, produces approximations of the right-hand side on the whole interval of definition and does not employ boundary conditions.

Key words: 
ordinary differential equation
regularization
Steklov discontinuous operator
References: 
  1. Ivanov V. K., Vasin V. V., Tanana V. P. Teoriia lineinykh nekorrektnykh zadach i ee prilozheniia [The theory of linear ill-posed problems and its applications]. Moscow, Nauka, 1978, 206 p. (in Russian).
  2. Denisov A. M. Vvedenie v teoriiu obratnykh zadach [Introduction to the theory of inverse problems]. Moscow, Moscow Univ. Press, 1994, 206 p. (in Russian).
  3. Khromov A. A., Khromova G. V. The Solution of the Problem of Determining the Dendity of Heat Sources in a Rod. Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2015, vol. 15, iss. 3, pp. 309–314. DOI: https://doi.org/10.18500/1816-9791-2015-15-3-309-314 (in Russian).
  4. Khromov A. A. Approximation of Function and Its Derivative by the Modificated Steklov Operator. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 4, pt. 2, pp. 593–597 (in Russian).
  5. Khromov A. P., Khromova G. V. Discontinuous Steklov operators in the problem of uniform approximation of derivatives on closed integral. Comput. Math. Math. Phys., 2014, vol. 54, no. 9, pp. 1389–1394. DOI: https://doi.org/10.1134/S0965542514090085
Received: 
17.01.2016
Accepted: 
28.05.2016
Published: 
30.06.2016
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