The problem of identifying the trajectory of a mobile point source in the convective transport equation
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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.
Convective transport equation, mobile point source, identification problem, source motion law, delta function approximation
Короткий адрес: https://sciup.org/147235243
IDR: 147235243 | DOI: 10.14529/mmp210208
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