Властивості інтегральних динамічних моделей у вигляді операторів і рівнянь типу Вольтерра

• Date: 2019
• Main Author: Фуртат, Юрій Олегович
• Format: Article
• Language: Ukrainian
• Published: Kamianets-Podilskyi National Ivan Ohiienko University 2019
• Online Access: http://mcm-tech.kpnu.edu.ua/article/view/184517
• Journal Title: Mathematical and computer modelling. Series: Technical sciences

Accuracy of dynamic object modeling results depends on the errors of different types: source data errors, calculation errors and model error. Errors of the primary data influence the accuracy of the result through the use and numerical implementation of the mathematical model. There are various forms of dynamic models, including ordinary differential equations, integral equations and operators, transfer functions, partial differential equations. The most common dynamic models for describing measurement processes are ordinary differential equations. But mathematical models in the form of integral equations have the advantage over them because, unlike differential equations, include the complete formulation of the problem together with the initial (boundary) conditions, they allow a one-size-fits-all approach to numerical solutions.An integral operator is an integral part of any integral equation that defines its basic properties. Many dynamical systems analysis problems result in mathe­matical models containing a linear integral Volterra operator, nonlinear Vol­terra-Hammerstein operators and Volterra-Urison operators. Volterra II-ty­pe integral equations, both linear and nonlinear, describe the problems of analy­zing a dynamic system with a pronounced unidirectional change in an indepen­dent variable, such as time. A typical example of such tasks is feedback systems.The analysis of the peculiarities of the integral method of mathematical modeling of dynamic objects shows that certain advantages of dynamic models in the form of integral equations and operators provide positive possibilities for constructing effective methods and means of creation, research, design and operation of measurement systems with integrated means of dynamic correction.