INFLUENCE OF SMOOTHNESS AND DISCRETISATION PARAMETERS ON THE ACCURACY OF NUMERICAL INTEGRATION OF TWO-DIMENSIONAL HIGHLY OSCILLATORY FUNCTIONS

Authors

  • O. P. Nechuiviter V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
  • Y. L. Khurdei V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
  • V. V. Ivanov V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
  • A. S. Shnitsar V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
  • O. R. Hishchak V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
  • A. V. Zabornyi V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
  • A. A. Letuta V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

DOI:

https://doi.org/10.15588/1607-3274-2026-2-4

Keywords:

digital twin, digital signal image processing, mathematical modeling, numerical integration, cubature formula, highly oscillating functions, interpolation of functions of many variables, sparse grid

Abstract

Context. Numerical integration of rapidly oscillating functions of several variables is a key concept in engineering models and digital image processing. Despite the availability of various integration methods, the influence of smoothness and discretisation parameters on the accuracy of approximation remains insufficiently studied.
Objective. The aim of this study is to analyze a cubature formula that uses economical interpolation schemes and to systematically investigate the influence of smoothness and discretisation parameters on the accuracy of numerical integration.
Method. There are methods for numerical integration of rapidly oscillating functions of several variables, which are developed
using information operators that restore intermediate values of functions based on known values of the function at points, lines, and planes. Such information operators include the operators of O. M. Lytvyn, on the basis of which economical schemes for interpolating functions of several variables have been created. Their application in constructing cubature formulas for approximate calculation of double integrals of rapidly oscillating functions of several variables of general form allows calculations to be performed with high accuracy. The main focus is on the question of how the estimation of the error of numerical integration of two-dimensional rapidly oscillating functions in general form improves with the increase in the smoothness of the function.
Results. The cubature formula of the approximate calculation of the double integral from the rapidly oscillating function of a general form is researched.
Conclusions. A comparative analysis of the accuracy of the cubature formula for different classes of functions showed that the class of differentiability of a function is a determining factor that influences the rate of decrease of the theoretical error of numerical integration. Economical interpolation schemes and a higher level of smoothness of functions provide a significant increase in the accuracy of approximate calculation of integrals of two-dimensional rapidly oscillating functions of general form

Author Biographies

O. P. Nechuiviter, V. N. Karazin Kharkiv National University, Kharkiv

Dr. Sc., Professor, Head of the Department of Information Computer Technologies and
Mathematics, Educational and Research Institute “Ukrainian Engineering and Pedagogical Academy”

Y. L. Khurdei, V. N. Karazin Kharkiv National University, Kharkiv

Senior Lecturer, Department of Information Computer Technologies and Mathematics, Educational and Research Institute “Ukrainian Engineering and Pedagogical Academy”

V. V. Ivanov, V. N. Karazin Kharkiv National University, Kharkiv

Post-graduate student at the Department of Information Computer Technology and Mathematics,
Educational and Research Institute “Ukrainian Engineering and Pedagogical Academy”

A. S. Shnitsar, V. N. Karazin Kharkiv National University, Kharkiv

Post-graduate student at the Department of Information Computer Technology and Mathematics,
Educational and Research Institute “Ukrainian Engineering and Pedagogical Academy”

O. R. Hishchak, V. N. Karazin Kharkiv National University, Kharkiv

Post-graduate student at the Department of Information Computer Technology and Mathematics,
Educational and Research Institute “Ukrainian Engineering and Pedagogical Academy”

A. V. Zabornyi, V. N. Karazin Kharkiv National University, Kharkiv

Post-graduate student at the Department of Information Computer Technology and Mathematics,
Educational and Research Institute “Ukrainian Engineering and Pedagogical Academy”

A. A. Letuta, V. N. Karazin Kharkiv National University, Kharkiv

Post-graduate student at the Department of Information Computer Technology and Mathematics,
Educational and Research Institute “Ukrainian Engineering and Pedagogical Academy”

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Published

2026-06-26

How to Cite

Nechuiviter, O. P. ., Khurdei, Y. L. ., Ivanov, V. V., Shnitsar, A. S. ., Hishchak, O. R., Zabornyi, A. V. ., & Letuta, A. A. . (2026). INFLUENCE OF SMOOTHNESS AND DISCRETISATION PARAMETERS ON THE ACCURACY OF NUMERICAL INTEGRATION OF TWO-DIMENSIONAL HIGHLY OSCILLATORY FUNCTIONS. Radio Electronics, Computer Science, Control, (2), 33–45. https://doi.org/10.15588/1607-3274-2026-2-4

Issue

No. 2 (2026): Radio Electronics, Computer Science, Control

Section

Mathematical and computer modelling

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Copyright (c) 2026 O. P. Nechuiviter, Y. L. Khurdei, V. V. Ivanov, A. S. Shnitsar, O. R. Hishchak, A. V. Zabornyi, A. A. Letuta

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