METHODS OF TECHNICAL SYSTEMS PARAMETERS’ CALCULATION

Abstract

This article solves many problems of optimal management of technical systems that contain sources of physical activity. These systems are systems with distributed parameters because for modeling and optimization of technological processes these systems use non-local boundary value problems with differential equations in partial derivatives. The solution of differential equations for such problems exists only in the standard form of the object of study, in the absence of a multilayer structure and ignoring the specific features of the thermal action process. It is necessary to solve boundary value problems non-classical differential equations to increase the accuracy of calculations and optimization of technical parameters of simulated processes. It is possible to justify the correctness of the boundary value problems using methods from the theory of generalized functions. Therefore, it is necessary to determine the conditions for the correctness of boundary value problems for specific types of differential equations. The optimization of parameters of the function for the substantiation the correctness of boundary value problems and applied optimization mathematical models will allow increased accuracy of calculations and optimization of parameters of the modeled systems.

The authors constructed a nonlocal boundary value problem of the system of differential equations of thermal conductivity considering the peculiarities of the process of thermal action on a multilayer material. The correctness of the boundary value problem in the space of generalized functions of power growth is substantiated by applying methods from the theory of generalized functions. The authors tested the conditions of restriction on the fundamental function of solutions in these spaces to prove the conditions for the existence of a single solution. The method proposed in the article should be used to solve applied problems in the calculation and optimization of technical, biotechnological, economic, and transport systems.