Approximation of a Function and Its Derivatives on the Basis of Cubic Spline Interpolation in the Presence of a Boundary Layer
- Authors: Blatov I.A.1, Zadorin A.I.2, Kitaeva E.V.3
-
Affiliations:
- Povolzhskiy State University of Telecommunications and Informatics
- Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences
- Samara University
- Issue: Vol 59, No 3 (2019)
- Pages: 343-354
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/180444
- DOI: https://doi.org/10.1134/S0965542519030047
- ID: 180444
Cite item
Abstract
The problem of approximate calculation of the derivatives of functions with large gradients in the region of an exponential boundary layer is considered. It is known that the application of classical formulas of numerical differentiation to functions with large gradients in a boundary layer leads to significant errors. It is proposed to interpolate such functions by cubic splines on a Shishkin grid condensed in the boundary layer. The derivatives of a function defined on the grid nodes are found by differentiating the cubic spline. Using this approach, estimates of the relative error in the boundary layer and the absolute error outside of the boundary layer are obtained. These estimates are uniform in a small parameter. The results of computational experiments are discussed.
About the authors
I. A. Blatov
Povolzhskiy State University of Telecommunications and Informatics
Author for correspondence.
Email: blatow@mail.ru
Russian Federation, Samara, 443010
A. I. Zadorin
Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences
Author for correspondence.
Email: zadorin@ofim.oscsbras.ru
Russian Federation, Novosibirsk, 630090
E. V. Kitaeva
Samara University
Email: zadorin@ofim.oscsbras.ru
Russian Federation, Samara, 443086
Supplementary files
