Numerical Method for Calculating Triple Integrals of Rapidly Oscillating Functions of General Form Using Data on a System of Planes - Нечуйвітер, Олеся; Іванов, Владислав; Шніцар, Андрій; Гіщак, Остап (Кам'янець-Подільський національний університет імені Івана Огієнка, 2026)
The current stage of technological development involves the rapid introduction of new digital technologies, algorithms and methods. Information technology has made it possible to adopt new approaches to the collection, processing and analysis of data. The introduction of new methods for obtaining input data requires the development of new algorithms and the creation of numerical methods to solve pressing problems. This leads to the need to create new or improve existing mathematical models and implement them effectively in computer systems. One of the key challenges in modern system and process modelling, particularly in digital image processing, is the numerical integration of functions of several variables. The main problem in the numerical integration of rapidly oscillating functions of several variables lies in deriving new volume integration formulas using multimodal data. Currently, there is interest in numerical integration methods developed using information operators, which reconstruct intermediate values of quantities based on a given set of known function values on planes, lines, at nodes of sparse grids, and so on. Such information operators include those of O. M. Lytvyn, the use of which has proven effective in the approximate calculation of Fourier coefficients of functions of two and three variables. The aim of this article is to construct and study, on the class of differentiable functions, a cubature formula for the approximate calculation of triple integrals of rapidly oscillating functions of general form. The cubature formula uses the traces of the functions on planes as input data. When constructing the cubature formula, piecewise-linear splines are used as auxiliary functions for the information operators