Geodesic
The problem of identifying the trajectory of a mobile point source in the convective transport equation
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 2, pp. 78-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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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: identification problem, source motion law, delta function approximation.
Mots-clés : convective transport equation, mobile point source 
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     title = {The problem of identifying the trajectory of a mobile point source in the convective transport equation},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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Kh. M. Gamzaev. The problem of identifying the trajectory of a mobile point source in the convective transport equation. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 2, pp. 78-84. http://geodesic.mathdoc.fr/item/VYURU_2021_14_2_a7/

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