Abstract:
The paper is devoted to approximate calculation of integrals of products of two functions by the method of tensor products of functionals. Under the assumption that one of them is from the Sobolev class with the dominant mixed derivative, and the other with fast oscillation, there are obtained unimprovable (in the sense of order) estimates of arising errors of approximation. Also, a comparative analysis with known methods in the "theory of oscillations" be conducted.
Keywords:
tensor product of functionals, Haar function, highly oscillatory integral, asymptotic method, Filon method, Levin collocation method.
Citation:
N. Temirgaliyev, S. S. Kudaibergenov, N. Zh. Nauryzbaev, “Orderly exact calculation of integrals of products of functions by the method of tenzor products of functionals”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 11, 94–99; Russian Math. (Iz. VUZ), 63:11 (2019), 83–87
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\by N.~Temirgaliyev, S.~S.~Kudaibergenov, N.~Zh.~Nauryzbaev
\paper Orderly exact calculation of integrals of products of functions by the method of tenzor products of functionals
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2019
\issue 11
\pages 94--99
\mathnet{http://mi.mathnet.ru/ivm9521}
\crossref{https://doi.org/10.26907/0021-3446-2019-11-94-99}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2019
\vol 63
\issue 11
\pages 83--87
\crossref{https://doi.org/10.3103/S1066369X19110124}
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Linking options:
https://www.mathnet.ru/eng/ivm9521
https://www.mathnet.ru/eng/ivm/y2019/i11/p94
This publication is cited in the following 1 articles:
S. S. Kudaibergenov, Ye. Ye. Nurmoldin, N. Zh. Nauryzbayev, N. Temirgaliyev, “Formulas for approximate calculation of the Chebyshev coefficients”, Russian Math. (Iz. VUZ), 65:2 (2021), 69–74
Citation in format AMSBIB
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