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Information × Registration Number 0219U004961, 0118U005229 , R & D reports Title To develop optimal quadrature formulas for the calculation of the Bessel transform popup.stage_title Head Zadiraka Valery Konstantinovich, Registration Date 19-12-2019 Organization V.M.Glushkov Institute of Cybernetics, National Academy of Science of Ukraine popup.description2 The obtained results continue the work of its performers on the creation of elements of the theory of optimal integration of rapidly-oscillating functions.The focus was on Bessel functions of the first kind, which are fast-oscillating at large values of their parameters, and because of the complexity of the problem of computing the Bessel transform, the results in this scientific field are not sufficiently varied, numerous, and complete. Integrals from rapidly-oscillating functions are widely used in the practice of mathematical modeling, in solving many modern engineering problems and numerical integration, which determines the relevance of this topic. In particular, there is a number of problems of mathematical physics, astronomy, elasticity theory, potential theory, the propagation of electromagnetic waves, thermal conductivity, applied statistics, etc., for solving which it is necessary to have effective algorithms for calculating the Bessel transform for accuracy and (or) speed. During the work, optimal in accuracy and close to them quadrature formulas of calculation of the Bessel transforms for five classes of integrand functions and other integrals of rapidly oscillating functions are developed, a priori estimates of the total error of the quadrature formulas on the classes of problems are obtained; algorithms for identifying, refining, measuring the values of the integrand in the Bessel transform are developed; T-efficient algorithms for computing the discrete Hankel transform are constructed. The scientific and practical significance of the results lies in the possibility, when using them, to reasonably choose or build algorithms that are effective in accuracy and (or) speed and the computing resources necessary for their implementation when calculating the Bessel transform with a given accuracy for a limited processor time. Product Description popup.authors Гнатів Лев Олексійович Коломис Олена Миколаївна Кондратенко Ольга Сергіївна Луц Василь Костянтинович Луц Лілія Володимирівна Нікітіна Ольга Юріївна Швідченко Інна Віталіївна Шевчук Богдан Михайлович popup.nrat_date 2020-04-02 Close