Control of the rod heating process in moving environment with volume heat formation

The article proposes a numerical method for solving the problem of controlling the process of heating a rod in moving environment with volume heat formation. The controlled parameter is the temperature at the left end of the rod. When constructing the control function, the approach is used, which is described in the works of V.I. Ukhobotov and I.V. Izmest‘ev. In this paper, special attention is paid to the development of a numerical method for solving the problem, as well as its software implementation. The approximation of the control problem is made using an implicit difference scheme. A program has been developed that allows one to obtain and visualize an approximate solution to the considered problem, as well as to build a control function. The performance of the program is verified on one example.