Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels
For the Volterra equations with analytic kernels, we establish the exact power order of complexity of their approximate solutions and show that the optimal power order is realized by the method of simple iterations based on the use of information in the form of the values of kernels and free terms a...
Збережено в:
| Дата: | 1994 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1994
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5592 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511822330724352 |
|---|---|
| author | Solodkii, S. G. Солодкий, С. Г. Солодкий, С. Г. |
| author_facet | Solodkii, S. G. Солодкий, С. Г. Солодкий, С. Г. |
| author_sort | Solodkii, S. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:14:13Z |
| description | For the Volterra equations with analytic kernels, we establish the exact power order of complexity of their approximate solutions and show that the optimal power order is realized by the method of simple iterations based on the use of information in the form of the values of kernels and free terms at certain points. In addition, for the Volterra equations with infinitely differentiable kernels, we determine the minimal order of the error of direct methods and construct a method which realizes this order. |
| first_indexed | 2026-03-24T03:19:00Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5592 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:19:00Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/6e/47a65dde4b9760930b88362fb9fc186e.pdf |
| spelling | umjimathkievua-article-55922020-03-19T09:14:13Z Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels Оптимизация алгоритмов приближенного решения уравнений Вольтерра с бесконечно дифференцируемыми ядрами Solodkii, S. G. Солодкий, С. Г. Солодкий, С. Г. For the Volterra equations with analytic kernels, we establish the exact power order of complexity of their approximate solutions and show that the optimal power order is realized by the method of simple iterations based on the use of information in the form of the values of kernels and free terms at certain points. In addition, for the Volterra equations with infinitely differentiable kernels, we determine the minimal order of the error of direct methods and construct a method which realizes this order. Знайдено точний степеневий порядок складності наближеного розв'язку рівнянь Вольтерра з аналітичними ядрами. Встановлено, що оіггимальний степеневий порядок реалізує метод простої ітерації, який використовує інформацію у вигляді значень ядра і вільного члена у точках. Крім того, для класів рівнянь Вольтерра з нескінченно диференційовними ядрами визначено мінімальний порядок похибки прямих методів і побудовано метод, що реалізує цей порядок. Institute of Mathematics, NAS of Ukraine 1994-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5592 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 11 (1994); 1534–1545 Український математичний журнал; Том 46 № 11 (1994); 1534–1545 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5592/7869 https://umj.imath.kiev.ua/index.php/umj/article/view/5592/7870 Copyright (c) 1994 Solodkii S. G. |
| spellingShingle | Solodkii, S. G. Солодкий, С. Г. Солодкий, С. Г. Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels |
| title | Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels |
| title_alt | Оптимизация алгоритмов приближенного решения уравнений Вольтерра с бесконечно дифференцируемыми ядрами |
| title_full | Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels |
| title_fullStr | Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels |
| title_full_unstemmed | Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels |
| title_short | Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels |
| title_sort | optimization of algorithms for the approximate solution of the volterra equations with infinitely differentiable kernels |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5592 |
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