Article

Optimal quadrature formulas for approximate calculation of rapidly oscillating integrals

Kholmat ShadimetovTashkent State Transport University, 1, Odilkhodjaev str., Tashkent, 100167, UzbekistanAnvar AdilkhodjaevTashkent State Transport University, 1, Odilkhodjaev str., Tashkent, 100167, UzbekistanOtabek GulomovNational Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”, 39, Kari Niaziy str., Tashkent, 100000, Uzbekistan

Results in Applied Mathematicsjournal2025en

ABI

Abstract

In this paper, we study the problem of constructing optimal formulas for approximate integration in the Sobolev space L 2 m ˜ 0 , 1 of periodic functions. Using the functional approach, we obtain optimal quadrature formulas for the approximate calculation of rapidly oscillating integrals. Then, we obtain explicit formulas for the coefficients of the optimal quadrature formulas and we get the sharp estimation of the error of the constructed formulas.

Topics

Mathematical functions and polynomials Electromagnetic Scattering and Analysis Numerical methods in engineering

Identifiers

DOI: 10.1016/j.rinam.2025.100627

Citations and references

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