Approximation of a Function and Its Derivatives on the Basis of Cubic Spline Interpolation in the Presence of a Boundary Layer
| Autor: | I. A. Blatov, A. I. Zadorin, E. V. Kitaeva |
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| Rok vydání: | 2019 |
| Předmět: |
Basis (linear algebra)
010102 general mathematics Mathematical analysis Function (mathematics) Grid 01 natural sciences Exponential function 010101 applied mathematics Computational Mathematics Boundary layer Approximation error Numerical differentiation 0101 mathematics Spline interpolation Mathematics |
| Zdroj: | Computational Mathematics and Mathematical Physics. 59:343-354 |
| ISSN: | 1555-6662 0965-5425 |
| DOI: | 10.1134/s0965542519030047 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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