On numerical approximation of system functions of control objects

The presented article is devoted to the use the finite element method to the problem of synthesis of control systems. In this research work, the weight (or system) function is considered. In this paper, we develop an algorithm to describe the synthesis of a finite element algorithm for a linear system function. The error of the results obtained using the finite element method are estimated with respect to to the most common numerical methods such as the Runge-Kutta method and the Euler method. This paper presents the results of simulation modeling. The publication compares the model outputs obtained using various numerical methods. The comparison demonstrates that the finite element method is as good as other numerical methods such as the Runge-Kutta method and the Euler method. The article presents the advantages of using the finite element method. These advantages include the ease of transition to uneven coverage of the computing area and high constructability, scalability, etc., especially revealing in the algorithmizing and programming of problems