Formulas for Numerical Differentiation on a Uniform Mesh in the Presence of a Boundary Layer Full article
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Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662 |
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| Output data | Year: 2024, Volume: 64, Number: 6, Pages: 1167-1175 Pages count : 9 DOI: 10.1134/s0965542524700416 | ||
| 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 considered. It is assumed that the original function of one variable can be decomposed into the sum of a regular component with bounded derivatives up to a certain order and a boundary layer component, which has large gradients and is known up to a factor. In particular, this decomposition is relevant for solution of a singularly perturbed boundary value problem, since the application of classical polynomial formulas of numerical differentiation to functions with large gradients can lead to significant errors. The error of numerical differentiation formulas is estimated for constructed formulas exact on the boundary layer component of the original function. The results of numerical experiments, consistent with the error estimates obtained, are presented.
Cite:
Zadorin A.I.
Formulas for Numerical Differentiation on a Uniform Mesh in the Presence of a Boundary Layer
Computational Mathematics and Mathematical Physics. 2024. V.64. N6. P.1167-1175. DOI: 10.1134/s0965542524700416 WOS Scopus РИНЦ OpenAlex
Formulas for Numerical Differentiation on a Uniform Mesh in the Presence of a Boundary Layer
Computational Mathematics and Mathematical Physics. 2024. V.64. N6. P.1167-1175. DOI: 10.1134/s0965542524700416 WOS Scopus РИНЦ OpenAlex
Original:
Задорин А.И.
Формулы численного дифференцирования на равномерной сетке при наличии пограничного слоя
Журнал вычислительной математики и математической физики. 2024. Т.64. №6. С.922-931. DOI: 10.31857/S0044466924060039 РИНЦ OpenAlex
Формулы численного дифференцирования на равномерной сетке при наличии пограничного слоя
Журнал вычислительной математики и математической физики. 2024. Т.64. №6. С.922-931. DOI: 10.31857/S0044466924060039 РИНЦ OpenAlex
Dates:
| Submitted: | Oct 13, 2023 |
| Accepted: | Mar 5, 2024 |
| Published print: | Jun 20, 2024 |
| Published online: | Jul 18, 2024 |
Identifiers:
| Web of science: | WOS:001272764600006 |
| Scopus: | 2-s2.0-85198920977 |
| Elibrary: | 68538388 |
| OpenAlex: | W4400777695 |
Citing:
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