Elements of the Theory of Optimal Integration of Highly Oscillating Functions on Classes of Functions
The elements of the theory of construction (with given information on the integral function) of the optimal quadrature formulas for calculating the integrals of highly oscillatory functions for certain classes of integral functions are presented. As oscillatory functions are considered: wavelet-func...
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| Date: | 2019 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Кам'янець-Подільський національний університет імені Івана Огієнка
2019
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| Online Access: | http://mcm-math.kpnu.edu.ua/article/view/174152 |
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| Journal Title: | Mathematical and computer modelling. Series: Physical and mathematical sciences |
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Mathematical and computer modelling. Series: Physical and mathematical sciences| Summary: | The elements of the theory of construction (with given information on the integral function) of the optimal quadrature formulas for calculating the integrals of highly oscillatory functions for certain classes of integral functions are presented. As oscillatory functions are considered: wavelet-function with compact carrier, — Bessel functions of the first kind of order m.The obtained results for the listed oscillatjry functions allowed us to create a theory of optimal integration of highly oscillatory functions both in classical formulation and for interpolation classes of functions.Considerable attention is paid to the identification and refinement of a priori information about the integral function and its use for narrowing the usual (classical) classes of integral functions to interpolation classes [1]. The functions included in such (interpolation) classes do not differ in quadrature formulas (the approximate integral value will be the same for them all).The second feature of the results is (in contrast to the results of all other authors) in the assumption of an approximate input of information about the integral function. Examining interpolation classes can increase the potential of quadrature formulas.Computer technologies (CTs) of the integration of highly oscillatory functions with given accuracy are analyzed. |
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