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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{VYURU_2021_14_2_a7,
     author = {Kh. M. Gamzaev},
     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},
     pages = {78--84},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2021_14_2_a7/}
}
TY  - JOUR
AU  - Kh. M. Gamzaev
TI  - The problem of identifying the trajectory of a mobile point source in the convective transport equation
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2021
SP  - 78
EP  - 84
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURU_2021_14_2_a7/
LA  - en
ID  - VYURU_2021_14_2_a7
ER  - 
%0 Journal Article
%A Kh. M. Gamzaev
%T The problem of identifying the trajectory of a mobile point source in the convective transport equation
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2021
%P 78-84
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURU_2021_14_2_a7/
%G en
%F VYURU_2021_14_2_a7
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/