Transformation of Mathematical Model for Complex Object in Form of Interval Difference Equations to a Differential Equation

Abstract

Mathematical models of complex objects in the form of interval difference equations are built on the basis of the obtained experimental interval data within the limits of the inductive approach. At the same time, interpretation of physical properties of the object on the base of such model is complex enough. A method of transformation of a mathematical model in the form of interval differential equations was proposed in the article. The proposed method is based on the formulas for representing the values of the function at the node of the difference grid in the Taylor series in the neighborhood of the base node, as well as the differential representation of the derivatives in the same neighborhood. The developed approach creates opportunities for the identification of interval models of complex objects based on the analysis of interval data with further interpretation of the physical properties of the modeled object according to the classical scheme.