Optimization of Approximate Integration Formulas for Periodic Function Classes

Authors

  • M.Kh. Shadimetov V.I.Romanovskiy Institute of Mathematics, AS RUz Author
  • S.S. Azamov Tashkent State Transport University Author
  • H.M. Kobilov Tashkent International University Author

DOI:

https://doi.org/10.71310/pcam.3_67.2025.10

Keywords:

optimal quadrature formula, Hilbert space, the error functional, Fourier transform

Abstract

This study explores the optimization of quadrature formulas for the approximate integration of periodic functions within a specific functional space. The research focuses on developing optimal quadrature formulas by deriving an analytical expression for the error associated with the integration process. By employing Fourier transform techniques and the concept of an extremal function, the study establishes a precise representation of the error. Additionally, optimal coefficients for the quadrature formula are determined to minimize this error, yielding an explicit solution. The results demonstrate enhanced accuracy compared to existing approaches, with the error characterized through a series expansion that reveals its asymptotic behavior. These findings advance the efficiency of numerical integration for periodic functions, offering potential applications in mathematical analysis, scientific computing, and related disciplines.

References

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Published

2025-07-27

Issue

No. 3(67) (2025)

Section

Статьи

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Copyright (c) 2025 M.Kh. Shadimetov

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This work is licensed under a Creative Commons Attribution 4.0 International License.