Development of new mathematical methods and algorithms for verifying the adequacy of mathematical models of objects based on data from a natural experiment to determine the functional stability area

The relevance of the development of applied mathematical modelling, which includes numerical methods and software packages in its problem area, its importance for the entire economic activity of the country as a whole, is due to the intensive digitalisation and computerisation of all technological chains of production processes. The integration of production support and various databases, as well as all parts of production and their effective management, require the development of comprehensive research of mathematical methods for modelling production processes. To date, mathematical modelling is applied to calculations of the financial stability point function, which does not fully reflect the variability of the predicted consequences, and consequently, the set of measures to preserve this stability. Due to the complication of production and economic relations, the need for modeling and calculating the area of financial stability, i.e., a set of marginal and non-marginal indicators, under which the economic condition of the enterprise will be considered to be acceptably stable, is actualised. The scientific problem is that mathematical modelling of production and economic processes does not provide for a wide variability (set) of indicators of financial stability as an area, which prevents flexivity in the economic activity of the enterprise. The scientific novelty of the work consists in the development of a method and algorithm for determining the financial stability area of an economic entity. The purpose of the study was to create a mathematical apparatus for calculating the financial stability of an enterprise. In the course of the study, the works of leading scientists and researchers in mathematical modelling and business processing, as well as the works of the authors of the article in this field were used. The authors presented a methodology for the development of quantitative indicators and, based on it, a methodology for mathematical modelling of calculating the financial stability area as a mathematical system that includes all eight main coefficients accepted as parameters of financial stability, and considers the limits that correspond to the economic indicators of the stability of the enterprise