The use of functions for mathematical modeling of transient processes

Introduction. The use of non-linear special functions is actual for the mathematical modeling of processes. If it is necessary to obtain the mathematical model of a particular variable processes according to the sum-total of statistical data, then the quality of the model greatly depends on the chosen form function, whose unknown parameters can be estimated, for example, by the method of least square method. Methods. Methods of mathematical modeling is applied. Results. We offer function whose reduction makes it possible to obtain linear dependence in relation to elementary functions of unknown parameters. Nonlinear functions that can be used to describe a monotonically increasing or monotonically decreasing character of dependence of the qualitative value of the process from the variable factors are examined, including those that have a point of change of their nature of the convexity (inflection point). The way of calculation of the characteristics of such functions using the method of the least squares is shown, in the case, if the obtained n discrete values of x correspond to the obtained n values of y. A comparative analysis of the approximation quality of the analytical functional dependency of the resulting value of yfrom the variable value x by functions of different types was conducted.