Non-Polynomial Interpolation of Functions with Large Gradients and Its Application
| Autor: | N. A. Zadorin, A. I. Zadorin |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Component (thermodynamics)
010102 general mathematics Order (ring theory) Function (mathematics) 01 natural sciences Polynomial interpolation 010101 applied mathematics Computational Mathematics Boundary layer Numerical differentiation Applied mathematics 0101 mathematics Interpolation Mathematics Variable (mathematics) |
| Zdroj: | Computational Mathematics and Mathematical Physics. 61:167-176 |
| ISSN: | 1555-6662 0965-5425 |
| DOI: | 10.1134/s0965542521020147 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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