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 J. Comp. Eng. Math., 2017, Volume 4, Issue 2, Pages 49–60 (Mi jcem90)

Computational Mathematics

About one numerical method for solving direct and inverse problems of the dynamic measurements theory

Yu. S. Popenko

South Ural State University (Chelyabinsk, Russian Federation)

Abstract: The direct and inverse problems of measurement theory based on linear differential operator with the boundary conditions of various types were considered. The boundary conditions are linear and linear independent functionals (including Cauchy problem, two-point boundary value problem, the Vallee-Poussin problem, the multipoint boundary value problems, the distributed data problems, and so on). An approach is proposed to investigate such problems on the basis of mathematical models realized in the form of linear boundary value problems and accompanying integral equations using the Green's function. The Green's functions, in the absence of information on the fundamental system of solutions of the corresponding differential equation, is constructed as a solution of the Fredholm integral equation of the second kind. The characteristics of the Fredholm equation were determined by the Green's function of the auxiliary problem. The proposed method allows to solve both the direct (the problem of finding solutions) and the inverse (the problem of finding the right-hand side of the equation from the experimentally obtained solution). The examples the work of programs realized in the system Mathematica 8.0 based on the described method were given.

Keywords: Green's function, nonlocal boundary conditions, measurements theory, dynamic measurements.

DOI: https://doi.org/10.14529/jcem170205

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Bibliographic databases:

UDC: 517.927.2
MSC: 34Â27
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Citation: Yu. S. Popenko, “About one numerical method for solving direct and inverse problems of the dynamic measurements theory”, J. Comp. Eng. Math., 4:2 (2017), 49–60

Citation in format AMSBIB
\Bibitem{Pop17} \by Yu.~S.~Popenko \paper About one numerical method for solving direct and inverse problems of the dynamic measurements theory \jour J. Comp. Eng. Math. \yr 2017 \vol 4 \issue 2 \pages 49--60 \mathnet{http://mi.mathnet.ru/jcem90} \crossref{https://doi.org/10.14529/jcem170205} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3670940} \elib{https://elibrary.ru/item.asp?id=29454745}