On the approximation by the poynomials of S. M. Bershtein type of the Hursa problem for nonlinear equation of hyperbolic type
Using Bernshtein type polynomials for functions of two variables, a scheme is given for successive approximations, and its uniform convergence to the unique solution of the Goursat problem for a nonlinear hyperbolic equation is proved.
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| Date: | 1992 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8044 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512886937354240 |
|---|---|
| author | Makhmudov , A. P. Le Dyk Kiem Махмудов , А. П. Ле Дык Кием |
| author_facet | Makhmudov , A. P. Le Dyk Kiem Махмудов , А. П. Ле Дык Кием |
| author_sort | Makhmudov , A. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-12-28T09:25:14Z |
| description | Using Bernshtein type polynomials for functions of two variables, a scheme is given for successive approximations, and its uniform convergence to the unique solution of the Goursat problem for a nonlinear hyperbolic equation is proved. |
| first_indexed | 2026-03-24T03:35:55Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-8044 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:35:55Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ae/67f73320e9be94b0064eee48abea98ae.pdf |
| spelling | umjimathkievua-article-80442023-12-28T09:25:14Z On the approximation by the poynomials of S. M. Bershtein type of the Hursa problem for nonlinear equation of hyperbolic type О приближении полиномами типа С. Н. Бернштейна решений задачи Гурса для нелинейного уравнения гиперболического типа Makhmudov , A. P. Le Dyk Kiem Махмудов , А. П. Ле Дык Кием Using Bernshtein type polynomials for functions of two variables, a scheme is given for successive approximations, and its uniform convergence to the unique solution of the Goursat problem for a nonlinear hyperbolic equation is proved. Используя многочлены типа С. Н. Бернштейна для функции двух переменных, предложена схема последовательных приближений и обоснована ее равномерная сходимость к единственному решению задачи Гурса для нелинейного гиперболического уравнения. Використовуючи многочлени типу С. Н. Бернштейна для функції двох змінних, запропонована схема послідовних наближень та обґрунтована її рівномірна збіжність до єдиного розв’язку задачі Гурса для нелінійного гіперболічного рівняння. Institute of Mathematics, NAS of Ukraine 1992-09-08 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8044 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 8 (1992); 1116-1123 Український математичний журнал; Том 44 № 8 (1992); 1116-1123 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/8044/9606 Copyright (c) 1992 A. P. Makhmudov , Le Dyk Kiem |
| spellingShingle | Makhmudov , A. P. Le Dyk Kiem Махмудов , А. П. Ле Дык Кием On the approximation by the poynomials of S. M. Bershtein type of the Hursa problem for nonlinear equation of hyperbolic type |
| title | On the approximation by the poynomials of S. M. Bershtein type of the Hursa problem for nonlinear equation of hyperbolic type |
| title_alt | О приближении полиномами типа С. Н. Бернштейна решений задачи Гурса для нелинейного уравнения гиперболического типа |
| title_full | On the approximation by the poynomials of S. M. Bershtein type of the Hursa problem for nonlinear equation of hyperbolic type |
| title_fullStr | On the approximation by the poynomials of S. M. Bershtein type of the Hursa problem for nonlinear equation of hyperbolic type |
| title_full_unstemmed | On the approximation by the poynomials of S. M. Bershtein type of the Hursa problem for nonlinear equation of hyperbolic type |
| title_short | On the approximation by the poynomials of S. M. Bershtein type of the Hursa problem for nonlinear equation of hyperbolic type |
| title_sort | on the approximation by the poynomials of s. m. bershtein type of the hursa problem for nonlinear equation of hyperbolic type |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8044 |
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