Quadratures with super power convergence
The calculation of quadratures arises in many physical and technical applications. The replacement of integration variables is proposed, which dramatically increases the accuracy of the formula of averages. For infinitely smooth integrand functions, the convergence law becomes super power. It is sig...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2023-12-01
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| Series: | Discrete and Continuous Models and Applied Computational Science |
| Subjects: | |
| Online Access: | https://journals.rudn.ru/miph/article/viewFile/35109/22190 |
| _version_ | 1797789067486691328 |
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| author | Aleksandr A. Belov Maxim A. Tintul Valentin S. Khokhlachev |
| author_facet | Aleksandr A. Belov Maxim A. Tintul Valentin S. Khokhlachev |
| author_sort | Aleksandr A. Belov |
| collection | DOAJ |
| description | The calculation of quadratures arises in many physical and technical applications. The replacement of integration variables is proposed, which dramatically increases the accuracy of the formula of averages. For infinitely smooth integrand functions, the convergence law becomes super power. It is significantly faster than the power law and is close to exponential one. For integrals with bounded smoothness, power convergence is realized with the maximum achievable order of accuracy. |
| first_indexed | 2024-03-13T01:45:30Z |
| format | Article |
| id | doaj.art-41bb767fee9c46459d191717b94231cc |
| institution | Directory Open Access Journal |
| issn | 2658-4670 2658-7149 |
| language | English |
| last_indexed | 2024-03-13T01:45:30Z |
| publishDate | 2023-12-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Discrete and Continuous Models and Applied Computational Science |
| spelling | doaj.art-41bb767fee9c46459d191717b94231cc2023-07-03T08:28:11ZengPeoples’ Friendship University of Russia (RUDN University)Discrete and Continuous Models and Applied Computational Science2658-46702658-71492023-12-0131212813810.22363/2658-4670-2023-31-2-128-13821014Quadratures with super power convergenceAleksandr A. Belov0https://orcid.org/0000-0002-0918-9263Maxim A. Tintul1https://orcid.org/0000-0002-5466-1221Valentin S. Khokhlachev2https://orcid.org/0000-0002-6590-5914M. V. Lomonosov Moscow State UniversityM. V. Lomonosov Moscow State UniversityM. V. Lomonosov Moscow State UniversityThe calculation of quadratures arises in many physical and technical applications. The replacement of integration variables is proposed, which dramatically increases the accuracy of the formula of averages. For infinitely smooth integrand functions, the convergence law becomes super power. It is significantly faster than the power law and is close to exponential one. For integrals with bounded smoothness, power convergence is realized with the maximum achievable order of accuracy.https://journals.rudn.ru/miph/article/viewFile/35109/22190trapezoid ruleexponential convergenceerror estimateasymptotically sharp estimates |
| spellingShingle | Aleksandr A. Belov Maxim A. Tintul Valentin S. Khokhlachev Quadratures with super power convergence Discrete and Continuous Models and Applied Computational Science trapezoid rule exponential convergence error estimate asymptotically sharp estimates |
| title | Quadratures with super power convergence |
| title_full | Quadratures with super power convergence |
| title_fullStr | Quadratures with super power convergence |
| title_full_unstemmed | Quadratures with super power convergence |
| title_short | Quadratures with super power convergence |
| title_sort | quadratures with super power convergence |
| topic | trapezoid rule exponential convergence error estimate asymptotically sharp estimates |
| url | https://journals.rudn.ru/miph/article/viewFile/35109/22190 |
| work_keys_str_mv | AT aleksandrabelov quadratureswithsuperpowerconvergence AT maximatintul quadratureswithsuperpowerconvergence AT valentinskhokhlachev quadratureswithsuperpowerconvergence |