Abstract: The issue of numerical differentiation of functions with large gradients is considered. It is assumed that there is a decomposition of a given function of one variable into a sum of a regular component and a boundary layer component; the latter is responsible for large gradients of the function and is known up to a factor. This decomposition is valid, in particular, for a solution of a singularly perturbed boundary value problem. However, the application of the classical polynomial formulas of numerical differentiation to functions with large gradients may produce significant errors. Numerical differentiation formulas that are exact on the boundary layer component are studied, and their error is estimated. Such formulas are proved to be more accurate than the classical ones in the case of the presence of a boundary layer component. An approach to estimating the error of the proposed formulas is suggested, and its applicability is shown in particular cases. The results of numerical experiments are presented. These results comply with the obtained error estimates and show an advantage in the accuracy of the proposed formulas.

Cite: Zadorin A.I.
Analysis of Numerical Differentiation Formulas on a Uniform Grid in the Presence of a Boundary Layer
Proceedings of the Steklov Institute of Mathematics. 2024. V.327. N1. P.S275–S285. DOI: 10.1134/S0081543824070204 WOS Scopus РИНЦ OpenAlex

Original: Задорин А.И.
Анализ формул численного дифференцирования на равномерной сетке при наличии пограничного слоя
Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN). 2024. Т.30. №4. С.106 - 116. DOI: 10.21538/0134-4889-2024-30-4-106-116 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Apr 4, 2024
Accepted:	May 13, 2024
Published print:	Mar 10, 2025
Published online:	Mar 10, 2025

Identifiers:

Web of science:	WOS:001447279100010
Scopus:	2-s2.0-105000029376
Elibrary:	80438668
OpenAlex:	W4408289299

Citing: Пока нет цитирований

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