Kh.M. Gamzaev
Èlektron. model. 2020, 42(1):25-32
https://doi.org/10.15407/emodel.42.01.025
ABSTRACT
The process of heating a one-dimensional rod by a movable heat source described by the parabolic equation with the right part is considered. The problem of identification of the trajectory of the mobile source for a given temperature regime at a given point of the rod is posed. This problem belongs to the class of inverse problems associated with the recovery of the right parts of partial differential equations. A discrete analogue of the problem is constructed using the usual finite-difference approximations in time and space. For the solution of the received difference problem the special representation allowing to split problems on three mutually independent difference problems of the second order is offered. The result is a quadratic equation for determining the position of the moving source for each discrete value of the time variable.
KEYWORDS
mobile source, the law of motion of the source, the source function, inverse problem, difference problem.
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