Formulas for numerical differentiation of functions with large gradients Full article
| Journal |
Numerical Analysis and Applications
ISSN: 1995-4239 |
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| Output data | Year: 2023, Volume: 16, Number: 1, Pages: 14-21 Pages count : 8 DOI: 10.1134/S1995423923010020 | ||
| Tags | function of one variable, large gradients, special formula for numerical differentiation, error estimate. | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН». | FWNF-2022-0016 |
Abstract:
Numerical differentiation of functions with large gradients is investigated. It is assumed that a function contains a component known up to a factor and responsible for the large gradients of the function. Application of classical formulas for calculating derivatives to such functions may lead to significant errors. Special-purpose formulas are studied for numerical differentiation on a uniform grid which are exact for a boundary layer component. Conditions are formulated under which an error estimate of a difference formula for a derivative does not depend on the gradients of the boundary layer component. In the case of an exponential boundary layer, when calculating a derivative of an arbitrarily given order error estimates that are uniform with respect to a small parameter are obtained. The results of numerical experiments are presented.
Cite:
Zadorin A.I.
Formulas for numerical differentiation of functions with large gradients
Numerical Analysis and Applications. 2023. V.16. N1. P.14-21. DOI: 10.1134/S1995423923010020 WOS Scopus РИНЦ OpenAlex
Formulas for numerical differentiation of functions with large gradients
Numerical Analysis and Applications. 2023. V.16. N1. P.14-21. DOI: 10.1134/S1995423923010020 WOS Scopus РИНЦ OpenAlex
Original:
Задорин А.И.
Формулы численного дифференцирования функций с большими градиентами
Сибирский журнал вычислительной математики. 2023. Т.26. №1. С.17-26. DOI: 10.15372/SJNM20230102 РИНЦ OpenAlex
Формулы численного дифференцирования функций с большими градиентами
Сибирский журнал вычислительной математики. 2023. Т.26. №1. С.17-26. DOI: 10.15372/SJNM20230102 РИНЦ OpenAlex
Dates:
| Submitted: | Sep 28, 2022 |
| Accepted: | Nov 23, 2022 |
| Published print: | Mar 21, 2023 |
| Published online: | Mar 21, 2023 |
Identifiers:
| Web of science: | WOS:000957143900002 |
| Scopus: | 2-s2.0-85150477483 |
| Elibrary: | 61082812 |
| OpenAlex: | W4328094943 |