In this paper, we have developed a method and an algorithm for solving the problem of the optimal selection of the density of heat sources on the rod in such a way that the temperature inside the considered area is within the specified limits is developed. In this case, the heat sources must provide the specified temperature regime of the minimum total power and temperature in the specified temperature corridor. Conservative finite-dimensional approximations of the original problem are constructed in the form of a linear programming problem. A method for constructing conservative difference schemes for solving the heat conduction equation with variable coefficients, a brief description of the developed software application for constructing computational grids and solving equations is presented. A new method for the numerical solution of non-stationary problems of optimal selection of heat sources in a rod is proposed and substantiated. A software application has been created for carrying out numerical experiments to solve the problem. The description of the based algorithm and the results of numerical experiments are given.
Хайиткулов Б.Х. Консервативные разностные схемы по оптимальному выбору местоположения источников тепла в стержне. Математическое моделирование и численные методы, 2020, № 3, с. 85–98.