Identification of discrete dynamic systems with distributed parameters

Background. The study is devoted to parametric identification of dynamic systems with distributed parameters, described by the difference equations. It was historically established that mathematical models of most physical phenomena and technical systems are described with differential equations (ordinary and with partial derivatives. To determine the coefficients of such equations it is possible to carry out only a finite number of measurements. Thus, if the equation coefficients are the functions of time or coordinates, it will be only possible to calculate them approximately. In such situation it is more natural to switch to equations in finite differences and to consider finite-difference models. More over, in many fields of physics and technology (aerodynamics, electrodynamics, geophysics) the discrete models are built initially. Due to this fact there is a necessity to develop methods of parametric identification of dynamic systems with distributed parameters, modeled by the difference equations. As far as the authors know, the present article is the first one considering the said problem. Materials and methods. The research is based on generalization of the difference equations of the Borel theorem on solution of integral equations of one class. Results. The authors suggest a general method of identification of parameters of dynamic systems with distributed parameters, modeled by the difference equations. Conclusions. The method may be applied in parametric identification of dynamic systems, mathematical models of which are described by differential equations with partial derivatives or by difference equations with many independent variables.