CONSERVATIVE SCHEMES OF THE NON-STATIONARY PROBLEM FOR THE OPTIMAL SELECTION OF THE LOCATION OF HEAT SOURCES IN THE ROD

In this paper, we develop a method and algorithm for solving the problem o f the optimal selection o f the density o f heat sources on the rod in such a way that the temperature inside the considered region is within the given limits. At the same time, heat sources must provide a given temperature regime o f the minimum total power and temperature in a given corridor. Conservative approximations o f the original problem are constructed in the form o f a linear programming problem. A method for constructing conservative schemes for solving the heat equation with variable coefficients, a brief description o f the developed software application for constructing computational grids and solving equations is given. A new method is proposed and justified for the numerical solution o f non-stationary problems o f the optimal selection o f heat sources in the rod. A software application for conducting numerical experiments to solve the problem has been created. A description o f the based algorithm and the results o f numerical experiments is provided.