Application of Cubic Splines on Bakhvalov Meshes in the Case of a Boundary Layer

Application of Cubic Splines on Bakhvalov Meshes in the Case of a Boundary Layer Full article

Journal

Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662

Output data

Year: 2021, Volume: 61, Number: 12, Pages: 1911-1930 Pages count : 20 DOI: 10.1134/S096554252112006X

Tags

Bakhvalov mesh; boundary layer; cubic spline; error estimate; modification; singular perturbation

Authors

Blatov I.A. ¹ , Zadorin A.I. ² , Kitaeva E.V. ³

Affiliations

1	Volga State University of Telecommunications and Informatics, Samara, 443010, Russian Federation
2	Sobolev Institute of Mathematics (Omsk Branch), Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation
3	Samara National Research University, Samara, 443086, Russian Federation

Funding (2)

1	Russian Foundation for Basic Research	20-01-00650
2	Sobolev Institute of Mathematics	0314-2019-0009

Abstract: The problem of cubic spline interpolation on Bakhvalov meshes for functions with high gradients is considered. Error estimates are obtained in the class of functions with high gradients in an exponential boundary layer. According to these estimates, the error of a spline can increase indefinitely as a small parameter tends to zero for a fixed number of grid nodes. A modified cubic interpolation spline is proposed, the error of which has an O(N- 4) estimate uniformly with respect to the small parameter, where $$N$$ is the number of grid nodes. © 2021, Pleiades Publishing, Ltd.

Blatov I.A. , Zadorin A.I. , Kitaeva E.V.
Application of Cubic Splines on Bakhvalov Meshes in the Case of a Boundary Layer
Computational Mathematics and Mathematical Physics. 2021. V.61. N12. P.1911-1930. DOI: 10.1134/S096554252112006X WOS Scopus OpenAlex

Web of science:	WOS:000742039500001
Scopus:	2-s2.0-85122955903
OpenAlex:	W4206036687

DB	Citing
Scopus	2
OpenAlex	2