NEW INFORMATION OPERATORS IN PROBLEMS OF NUMERICAL INTEGRATION OF FUNCTIONS OF THREE VARIABLES

Abstract

The rapid development and implementation of the latest information technologies in many fields of science and technology contribute to the rise of new methods in mathematical modeling of systems and processes. In particular, new mathematical theories have appeared that can be effectively used for building and improvement of existing mathematical models of various phenomena and objects. One of these theories is the theory of new information operators, authored by the Laureate of the State Prize of Ukraine in Science and Technology, doctor of physical and mathematical sciences, professor (думаю, это излишняя информация в аннотации) O. M. Lytvyn. New information operators have found their application in the digital processing of signals and images, namely in the numerical integration of rapidly oscillating functions of many variables. Cubature formulas were built that are optimal in the order of accuracy and use the value of the non-oscillating factor of the integrand function not only at points, but also on planes or lines. The article demonstrates the application of new information operators to the numerical integration of functions of many variables, namely, the issue of approximate calculation of the integral from functions of three variables is considered in the case when the information about the function is given by its traces on the lines. The cubature formula uses an interlineation operator built on the basis of an interflatation operator with auxiliary functions in the form of piecewise constant splines. An estimate of the approximation error of the proposed cubature formula on the class of differentiable functions was obtained. The results of the calculation experiment in the computer mathematics system Mathcad are presented. Numerical calculations confirm the theoretical statements of the study.