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

  • GENERAL NUMERICAL METHODS
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Abstract

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 \(O(1)\), 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.

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Funding

This work was supported by the Russian Foundation for Basic Research (Sections 1, 2, and 4, project no. 20-01-00650; Sections 3, 5, and 6, project no. 19-31-60009).

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. I. Zadorin & N. A. Zadorin

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  1. A. I. Zadorin
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  2. N. A. Zadorin
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Correspondence to A. I. Zadorin or N. A. Zadorin.

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Translated by E. Chernokozhin

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Zadorin, A.I., Zadorin, N.A. Non-Polynomial Interpolation of Functions with Large Gradients and Its Application. Comput. Math. and Math. Phys. 61, 167–176 (2021). https://doi.org/10.1134/S0965542521020147

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  • DOI: https://doi.org/10.1134/S0965542521020147

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