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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2021, Volume 14, Issue 2, Pages 78–84 (Mi vyuru597)  

Short Notes

The problem of identifying the trajectory of a mobile point source in the convective transport equation

Kh. M. Gamzaev

Azerbaijan State Oil and Industry University, Baku, Azerbaijan

Abstract: We consider the problem of identifying the trajectory of a mobile point source described by the Delta function in a one-dimensional linear convective transport equation under a given additional boundary condition. To solve this problem, the Delta function is approximated by a continuous function and a discrete analog of the problem is constructed using finite-difference approximations in the form of an implicit difference scheme. To solve the resulting difference problem, we propose a special representation that allows to split the problem into two mutually independent linear first-order difference problems at each discrete value of a time variable. The result is an explicit formula for determining the position of a mobile point source for each discrete value of a time variable. Based on the proposed computational algorithm, numerical experiments were performed for model problems.

Keywords: convective transport equation, mobile point source, identification problem, source motion law, delta function approximation.

DOI: https://doi.org/10.14529/mmp210208

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UDC: 519.63
MSC: 65M32; 80A23
Received: 18.12.2020
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Citation: Kh. M. Gamzaev, “The problem of identifying the trajectory of a mobile point source in the convective transport equation”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 14:2 (2021), 78–84

Citation in format AMSBIB
\Bibitem{Gam21}
\by Kh.~M.~Gamzaev
\paper The problem of identifying the trajectory of a mobile point source in the convective transport equation
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2021
\vol 14
\issue 2
\pages 78--84
\mathnet{http://mi.mathnet.ru/vyuru597}
\crossref{https://doi.org/10.14529/mmp210208}


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