The optimization of computational methods in function spaces is one of the main problems in computational mathematics. In this work, using the variational method optimization of difference formulas for an approximate solution to the Cauchy problem is given. It is known that the errors of difference formulas are estimated from above using the norm of the error functional of these formulas. To find the norm of the error functional of difference formulas in explicit form, we will use the so-called extremal function of this functional. Here we will find the extremal function of this functional in a specific Hilbert space. A system of equations of the Wiener-Hopf type will be obtained by minimizing the squared norm of the error functional of difference formulas by coefficients. Next, we will prove the existence and uniqueness of a solution to this system.
| Mualliflar | Shadimetov, Kh.M., Karimov, R.S., Шадиметов, Х.М., Каримов, Р.С. |
|---|---|
| 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 | 2024-12-11 |
| Son | 4/1 |
| Betlar | 74-84 |
| Til | Ingliz |
| Indeksga qo‘shilgan | 2026-08-27 |
Hilbert space, Cauchy problem, the extremal function, the error functional, optimal difference formula, пространство Гильберта, задача Коши, экстремальная функция, функционал погрешности, оптимальная разностная формула
| APA | Shadimetov, Kh.M., Karimov, R.S., Шадиметов, Х.М., & Каримов, Р.С. (2024). Wiener–Hopf type system for finding optimal coefficients of difference formulas in the Hilbert space. Ҳисоблаш ва амалий математика муаммолари, (4/1), 74-84. https://journals.airi.uz/index.php/pvpm/article/view/50 |
|---|---|
| GOST (OAK) | Shadimetov, Kh.M. va b. Wiener–Hopf type system for finding optimal coefficients of difference formulas in the Hilbert space // Ҳисоблаш ва амалий математика муаммолари. – 2024. – № 4/1. – P. 74-84. |
| MLA | Shadimetov, Kh.M., Karimov, R.S., Шадиметов, Х.М., and Каримов, Р.С. “Wiener–Hopf type system for finding optimal coefficients of difference formulas in the Hilbert space.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 74-84, 2024. https://journals.airi.uz/index.php/pvpm/article/view/50 |
| Chicago | Shadimetov, Kh.M., Karimov, R.S., Шадиметов, Х.М., and Каримов, Р.С. “Wiener–Hopf type system for finding optimal coefficients of difference formulas in the Hilbert space.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 74-84 (2024). https://journals.airi.uz/index.php/pvpm/article/view/50 |
| Harvard | Shadimetov, Kh.M., Karimov, R.S., Шадиметов, Х.М., and Каримов, Р.С (2024) ‘Wiener–Hopf type system for finding optimal coefficients of difference formulas in the Hilbert space’, Ҳисоблаш ва амалий математика муаммолари, (4/1), 74-84. https://journals.airi.uz/index.php/pvpm/article/view/50 |
| BibTeX | @article{shadimetovkhm2024,
title = {Wiener–Hopf type system for finding optimal coefficients of difference formulas in the Hilbert space},
author = {Shadimetov, Kh.M. and Karimov, R.S. and Шадиметов, Х.М. and Каримов, Р.С.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2024},
number = {4/1},
pages = {74-84},
url = {https://journals.airi.uz/index.php/pvpm/article/view/50}
} |
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