O‘zbekiston matematika jurnali Volume 70 Issue 2 (2026) · pp. 199-207

Optimization of the Euler-Maclaurin type quadrature formula in the Hilbert space of periodic functions

Usmanov, Kh.I.

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Abstract

This paper proposes a method for solving the problems of the Euler - Bernoulli beam, in which the problem is reduced to the solution of the Fredholm integral equation of the second kind. This integral equation is solved by the method of optimal quadrature formulas with derivatives. Then,using the Green function, the analytic solution is determined. Different boundary conditions can be used to determine the numerical and analytical solutions. results from other researchers to illustrate the performance of the proposed method

differential equation, integral equation, optimal quadrature formula, beam deflection value, absolute error

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Cite

APA 7 
Usmanov, Kh.I. (2026). Optimization of the Euler-Maclaurin type quadrature formula in the Hilbert space of periodic functions. O‘zbekiston matematika jurnali, 70(2), 199-207.
GOST R 7.0.5 
Usmanov, Kh.I. Optimization of the Euler-Maclaurin type quadrature formula in the Hilbert space of periodic functions // O‘zbekiston matematika jurnali. 2026. Т. 70. № 2. С. 199-207.
BibTeX 
@article{kh.i.2026,
  author  = {Usmanov, Kh.I.},
  title   = {Optimization of the Euler-Maclaurin type quadrature formula in the Hilbert space of periodic functions},
  journal = {O‘zbekiston matematika jurnali},
  year    = {2026},
  volume  = {70},
  number  = {2},
  pages   = {199-207}
}
RIS 
TY  - JOUR
AU  - Usmanov, Kh.I.
TI  - Optimization of the Euler-Maclaurin type quadrature formula in the Hilbert space of periodic functions
JO  - O‘zbekiston matematika jurnali
PY  - 2026
VL  - 70
IS  - 2
SP  - 199
EP  - 207
ER  -