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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 1, Pages 72–85
DOI: https://doi.org/10.33048/semi.2023.20.007
(Mi semr1571)
 

Differentical equations, dynamical systems and optimal control

Iterative solution of the retrospective inverse heat conduction problem using the Poisson integral

V. I. Vasiliev, A. M. Kardashevsky

North-Eastern Federal University, str. Belinskogo, 58, 677000, Yakutsk, Russia
References:
Abstract: This paper considers the inverse problem of identification of the finite initial condition of the Cauchy problem for the homogeneous heat conduction equation using the first kind linear Fredholm integral equation. Its discretization is carried out with the help of the quadrature rectangular formula. For the numerical realization of the obtained system of linear algebraic equations with almost complete, symmetric, positively determined, ill-conditioned matrix it is proposed to use the method of conjugate gradients. Examples of reconstruction of smooth, nonsmooth and discontinuous initial conditions in one- and two-dimensional cases, including the introduction of «noise», characteristic of redefinition conditions of inverse problems, are given.
Keywords: retrospective inverse heat conduction problem, Poisson integral, first kind Fredholm integral equation, system of linear equations with ill-conditioned matrix, method of conjugate gradients.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 14.Y26.31.0013
075-02-2022-881
Received August 31, 2021, published February 13, 2023
Document Type: Article
UDC: 519.6
MSC: 65M32,65R32
Language: Russian
Citation: V. I. Vasiliev, A. M. Kardashevsky, “Iterative solution of the retrospective inverse heat conduction problem using the Poisson integral”, Sib. Èlektron. Mat. Izv., 20:1 (2023), 72–85
Citation in format AMSBIB
\Bibitem{VasKar23}
\by V.~I.~Vasiliev, A.~M.~Kardashevsky
\paper Iterative solution of the retrospective inverse heat conduction problem using the Poisson integral
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 1
\pages 72--85
\mathnet{http://mi.mathnet.ru/semr1571}
\crossref{https://doi.org/10.33048/semi.2023.20.007}
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