Numerical integration of Fourier integrals by the optimal quadrature formula exact for hyperbolic functions
A.R. HayotovNational University of Uzbekistan named after Mirzo Ulugbek, 4, University str., Tashkent 100174, UzbekistanAbdimumin KurbonnazarovV.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, University str., Tashkent 100174, UzbekistanSarvarbek Z. PolvonovBukhara State University, 11, M.Ikbol str., Bukhara 200114, Uzbekistan
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Annotatsiya
This paper studies the problem of construction of the optimal quadrature formula for numerical calculation of Fourier integrals. Applying the discrete analogue of the differential operator d4dx4−2d2dx2+1 and using its properties we obtain the optimal quadrature formula wich is exact for hyperbolic functions sinh(x) and cosh(x), we get explicit expressions for the coefficients of the optimal quadrature formula. The obtained optimal quadrature formulas can be used in problems where Fourier transformations are used.
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