Many mathematical models in science and technology have been reduced to the approximate calculation of singular integrals with Cauchy and Hilbert kernels and the approximate solution of integral equations. In this paper, an optimal quadrature formula for approximate calculation of singular integrals with a Hilbert kernel in the Sobolev space is constructed and analytical formulas for coefficients that minimize its error are obtained from among the coefficients of the quadrature formula. For this, the discrete analogue of the second-order differential operator is used. The resulting quadrature formula is exact to a first-order polynomial.
| Mualliflar | Shadimetov, Kh.M., Jabborov, Kh.Kh., Шадиметов, Х.М., Жабборов, Х.Х. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2025-01-03 |
| Son | 4/2 |
| Betlar | 5-14 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-27 |
singular integral, Hilbert kernel, error functional, optimal quadrature formula, extremal function, differential operator, optimal coefficients, сингулярный интеграл с ядром Гильберта, функционал погрешности, оптимальная квадратурная формула, экстремальная функция, дифференциальный оператор, оптимальные коэффициенты
| APA | Shadimetov, Kh.M., Jabborov, Kh.Kh., Шадиметов, Х.М., & Жабборов, Х.Х. (2025). Optimal Quadrature Formula for Approximate Calculation of Singular Integrals with Hilbert kernel. Ҳисоблаш ва амалий математика муаммолари, (4/2), 5-14. https://journals.airi.uz/index.php/pvpm/article/view/58 |
|---|---|
| GOST (OAK) | Shadimetov, Kh.M. va b. Optimal Quadrature Formula for Approximate Calculation of Singular Integrals with Hilbert kernel // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 4/2. – P. 5-14. |
| MLA | Shadimetov, Kh.M., Jabborov, Kh.Kh., Шадиметов, Х.М., and Жабборов, Х.Х. “Optimal Quadrature Formula for Approximate Calculation of Singular Integrals with Hilbert kernel.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 5-14, 2025. https://journals.airi.uz/index.php/pvpm/article/view/58 |
| Chicago | Shadimetov, Kh.M., Jabborov, Kh.Kh., Шадиметов, Х.М., and Жабборов, Х.Х. “Optimal Quadrature Formula for Approximate Calculation of Singular Integrals with Hilbert kernel.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 5-14 (2025). https://journals.airi.uz/index.php/pvpm/article/view/58 |
| Harvard | Shadimetov, Kh.M., Jabborov, Kh.Kh., Шадиметов, Х.М., and Жабборов, Х.Х (2025) ‘Optimal Quadrature Formula for Approximate Calculation of Singular Integrals with Hilbert kernel’, Ҳисоблаш ва амалий математика муаммолари, (4/2), 5-14. https://journals.airi.uz/index.php/pvpm/article/view/58 |
| BibTeX | @article{shadimetovkhm2025,
title = {Optimal Quadrature Formula for Approximate Calculation of Singular Integrals with Hilbert kernel},
author = {Shadimetov, Kh.M. and Jabborov, Kh.Kh. and Шадиметов, Х.М. and Жабборов, Х.Х.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {4/2},
pages = {5-14},
url = {https://journals.airi.uz/index.php/pvpm/article/view/58}
} |
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