New Approach to Modeling Dynamic Objects

A new approach to mathematical modeling of dynamic objects is presented. This approach is based on the use of a new idea of a quantitative estimation of the time variation of the nature of the particular solution of a system of ordinary differential equations describing a simulated object. This change in the nature of the solution is typical for stiff systems of equations. Such an estimation allows for the correction of the state variables characterizing the object to ensure the stability of numerical methods for solving the Cauchy problems. This correction, in particular, makes it possible to use explicit methods for analyzing an object that are characterized by low computational costs, but which are practically ineffective in the case of stiff systems of equations. The quantitative estimation also allows us to identify the characteristic modes of operation of dynamic objects without solving the Cauchy problem. The results of numerical experiments based on the approach presented that prove its high efficiency.