Cubature Formulas for Oscillatory Integrals with Given Function Traces on Lines - Khurdei, Yevheniia; Ivanov, Vladyslav (Kìbernetika ta komp'ûternì tehnologìï (Online), 2025)
Introduction. Numerical integration of rapidly oscillating multivariable functions plays an important role in applied mathematics, particularly in image processing, computed tomography, and mathematical modeling. Traditional integration methods often prove inefficient in cases involving complex function structures and limited input data. Under such conditions, methods that utilize function traces on lines become especially relevant. The purpose is to construct a cubature formula for the approximate evaluation of triple integrals of trigonometric functions defined on Holder and Lipschitz classes using function traces on lines. To obtain corresponding approximation error estimates. Results. An approach for constructing cubature formulas for approximate evaluation of triple integrals of trigonometric functions is developed, based on the use of function traces on lines and the information operators of O.M. Lytvyn. Error estimates of the numerical integration formula are proved for Holder and Lipschitz function classes. Conclusions. The proposed method enables approximate computation of triple trigonometric integrals based on given function values along lines. The results can be applied in numerical analysis and mathematical modeling problems requiring integration of rapidly oscillating functions of general form. Keywords: numerical integration of multivariable functions, rapidly oscillating multivariable functions, cubature formulas, digital image processing.