Calculation of Double Integrals of Oscillating Exponential Functions from Data on Lines

• Дата: 2026
• Автори: Хурдей, Євгенія, Нефьодова, Інна, Заборний, Антон, Летута, Андрій
• Формат: Стаття
• Мова: Українська
• Опубліковано: Кам'янець-Подільський національний університет імені Івана Огієнка 2026
• Онлайн доступ: https://mcm-math.kpnu.edu.ua/article/view/354926
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

Modern mathematical modelling of physical and technical processes currently involves solving the problem of processing and analysing functions of several variables, the values of which are known along lines. This problem is relevant in digital image processing, as a significant portion of the information about the object under study may be obtained in the form of measurements along individual directions or lines, which is characteristic of tomographic methods, remote sensing and visualisation systems. Within the scope of solving such problems, the problem of numerical integration of oscillating functions based on data on a system of lines is of considerable interest. One of the subproblems of this problem is the integration of oscillating exponential functions of several variables. The research in this article is devoted to the numerical integration of oscillating exponential functions of two variables. A cubature formula for the approximate calculation of double integrals of an oscillating exponential is presented. In its construction, the cubature formula utilises traces on mutually perpendicular lines as data on the function. Error estimates for the approximation are presented in the Hölder and Lipschitz classes. The paper devotes considerable attention to testing the cubature formula for the approximate calculation of double integrals of an oscillating exponential. The results obtained confirm the theoretical error estimates in the Lipschitz and Hölder classes. In the numerical experiment, an elliptical tomographic phantom was used as the test function. The chosen test function has an important property: the corresponding integral of such a function has an analytical representation, which allows one to obtain correct reference values of the integral. The paper presents a detailed analysis of the influence of the oscillation parameter ω and the partition ℓ on the accuracy of numerical integration of oscillating exponential functions of two variables.