Non-Polynomial Interpolation of Functions with Large Gradients and Its Application

Interpolation of a function of one variable with large gradients in the boundary layer region is studied. The problem is that the use of classical polynomial interpolation formulas on a uniform mesh to functions with large gradients can lead to errors of the order of , despite a small mesh size. An...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2021-02, Vol.61 (2), p.167-176
Main Authors: Zadorin, A. I., Zadorin, N. A.
Format: Article
Language:English
Subjects:
Boundary layers
Computational Mathematics and Numerical Analysis
Error analysis
Functions (mathematics)
General Numerical Methods
Interpolation
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical differentiation
Polynomials
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Summary:Interpolation of a function of one variable with large gradients in the boundary layer region is studied. The problem is that the use of classical polynomial interpolation formulas on a uniform mesh to functions with large gradients can lead to errors of the order of , despite a small mesh size. An interpolation formula based on fitting to the component that defines the boundary-layer growth of the function is investigated. An error estimate, which depends on the number of interpolation nodes and is uniform over the boundary layer component and its derivatives, is obtained. It is shown how the interpolation formula derived can be used to construct formulas for numerical differentiation and integration and in the two-dimensional case. The corresponding error estimates are obtained.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542521020147