Забезпечення бажаного порядку локальної похибки при реалізації моделей динамічних систем методом зі зростаючою точністю

• Datum: 2025
• Hauptverfasser: Положаєнко, Сергій, Прокофьев, Андрій
• Format: Artikel
• Sprache: Ukrainian
• Veröffentlicht: Kamianets-Podilskyi National Ivan Ohiienko University 2025
• Online Zugang: http://mcm-tech.kpnu.edu.ua/article/view/332626
• Назва журналу: Mathematical and computer modelling. Series: Technical sciences

One of the main qualitative indicators of computing tools is the accuracy of the results of solving applied problems, in particular, problems of modelling and control of dynamic systems. However, despite the widespread use of computing tools (CT), the problem of assessing the accuracy of calculations cannot be considered solved, and its relevance is increasing due to the rapid development and spread of cybernetic tools for various purposes. The severity of the problem lies in the complexity of the analysis of calculation errors, which leads to the cumbersomeness of analytical justifications and a large amount of calculations required to obtain specific numerical data. To solve many technical and scientific research problems, both universal and specialized OT tools are widely used. A characteristic difference of the latter from universal OT tools is a deliberately narrow class of algorithms that are implemented, focused on solving a limited range of applied problems. In this case, of course, it is expected to achieve a number of certain (compared to universal OT tools) advantages, which usually include one or a group of factors, such as increased speed, non-analytical method of solving problems (for analog specialized OT tools), reduced weight and dimensions and cost, etc. It should be noted that the problem of accuracy is relevant for both universal and specialized OT tools, somewhat transforming, depending on the type of tool and the principle of its operation, for example, the originality of the initial errors. As a way to simplify the no less laborious process of analyzing the accuracy of the result following the problem-solving process (or to increase its efficiency), it is possible to present the transfer of at least part of this (last) process to the period preceding the solution of the main problem. This way consists in the preliminary calculation of the dependences of the error, and, practically, its characteristics, on the characteristics of the primary errors associated with the implementation, in particular, of mathematical models (MM) of dynamic systems in applied problems of their modelling and control.