Lagrange Interpolation and the Newton–Cotes Formulas on a Bakhvalov Mesh in the Presence of a Boundary Layer Full article
| Journal |
Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662 |
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| Output data | Year: 2022, Volume: 62, Number: 3, Pages: 347-358 Pages count : 12 DOI: 10.1134/S0965542522030149 | ||
| Tags | Bakhvalov mesh; boundary layer; error estimate; function of one variable; Lagrange interpolation polynomial | ||
| Authors |
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| Affiliations |
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Funding (3)
| 1 | Russian Foundation for Basic Research | 20-01-00650 |
| 2 | Russian Foundation for Basic Research | 19-31- 60009 |
| 3 | Sobolev Institute of Mathematics | 0314-2019-0009 |
Abstract:
Abstract: Application of a Lagrange polynomial on a Bakhvalov mesh for the interpolation of a function with large gradients in an exponential boundary layer is studied. The problem is that the use of a Lagrange polynomial on a uniform mesh for interpolation of such a function can lead to errors of order O(1), despite the smallness of the mesh size. The Bakhvalov mesh is widely used for the numerical solution of singularly perturbed problems, and the analysis of interpolation formulas on such a mesh is of interest. Estimates of the error of interpolation by a Lagrange polynomial with an arbitrary number of interpolation nodes on a Bakhvalov mesh are obtained. The result is used to estimate the error of the Newton–Cotes formulas on a Bakhvalov mesh. The results of numerical experiments are presented.
Cite:
Zadorin A.I.
, Zadorin N.A.
Lagrange Interpolation and the Newton–Cotes Formulas on a Bakhvalov Mesh in the Presence of a Boundary Layer
Computational Mathematics and Mathematical Physics. 2022. V.62. N3. P.347-358. DOI: 10.1134/S0965542522030149 WOS Scopus РИНЦ OpenAlex
Lagrange Interpolation and the Newton–Cotes Formulas on a Bakhvalov Mesh in the Presence of a Boundary Layer
Computational Mathematics and Mathematical Physics. 2022. V.62. N3. P.347-358. DOI: 10.1134/S0965542522030149 WOS Scopus РИНЦ OpenAlex
Original:
Задорин А.И.
, Задорин Н.А.
Интерполяция Лагранжа и формулы Ньютона-Котеса на сетке Бахвалова при наличии пограничного слоя
Журнал вычислительной математики и математической физики. 2022. Т.62. №3. С.355-366. DOI: 10.31857/S0044466922030140 РИНЦ OpenAlex
Интерполяция Лагранжа и формулы Ньютона-Котеса на сетке Бахвалова при наличии пограничного слоя
Журнал вычислительной математики и математической физики. 2022. Т.62. №3. С.355-366. DOI: 10.31857/S0044466922030140 РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000783044700001 |
| Scopus: | 2-s2.0-85128314615 |
| Elibrary: | 48429400 |
| OpenAlex: | W4224054674 |