Parabolic spline interpolation for functions with large gradient in the boundary layer

Blatov I. A.; Zadorin A. I.; Kitaeva E. V.

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Parabolic spline interpolation for functions with large gradient in the boundary layer

机译：抛物线样条插值在边界层中具有大梯度的函数

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摘要

We consider the problem of Subbotin's parabolic spline interpolation for functions with large gradient domains. In the case of the common piecewise uniform Shishkin's mesh we obtain two-sided accuracy estimates for the class of functions with exponential boundary layer. The spline interpolation accuracy estimates are not uniform in a small parameter, while the error itself can grow unboundedly as the small parameter vanishes and the number N of nodes remains fixed. We include the results of some simulations.

机译：我们考虑亚比丁抛物线样条插值的问题，用于具有大梯度域的功能。在公共分段均匀的Shishkin的网格中，我们获得了指数边界层的函数类的双面精度估计。花键插值精度估计在一个小参数中并不均匀，而错误本身可以随着小参数消失，并且节点的数字n保持固定。我们包括一些模拟的结果。

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来源
《Siberian Mathematical Journal》 |2017年第4期|共13页
作者
Blatov I. A.; Zadorin A. I.; Kitaeva E. V.;
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作者单位

Volga State Univ Telecommun &

Informat Samara Russia;

Sobolev Inst Math Omsk Branch Omsk Russia;

Samara Natl Res Univ Samara Russia;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
boundary layer; large gradient; parabolic spline; Shishkin mesh; interpolation accuracy;

机译：边界层;大梯度;抛物线样条曲线;Shishkin网格;插值准确性;

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专利

1. Parabolic spline interpolation for functions with large gradient in the boundary layer [J] . Blatov I. A., Zadorin A. I., Kitaeva E. V. Siberian Mathematical Journal . 2017,第4期

机译：抛物线样条插值在边界层中具有大梯度的函数
2. On the Uniform Convergence of Parabolic Spline Interpolation on the Class of Functions with Large Gradients in the Boundary Layer [J] . I. A. Blatov, A. I. Zadorin, E. V. Kitaeva Numerical analysis and applications . 2017,第2期

机译：论边界层大梯度抛物线样条插值的统一收敛
3. Generalized Spline Interpolation of Functions with Large Gradients in Boundary Layers [J] . Blatov I. A., Zadorin A. I., Kitaeva E. V. Computational mathematics and mathematical physics . 2020,第3期

机译：广域层中大梯度函数的广义样条插值
4. On the parabolic spline-interpolation of functions with a boundary layer [C] . LA. Blatov, E.V. Kitaeva International Conference on Information Technology and Nanotechnology . 2017

机译：关于边界层函数的抛物线样条插值
5. Boundary and internal layers in a semilinear parabolic problem. [D] . Salazar-Gonzalez, Jose Domingo. 1998

机译：半线性抛物线问题中的边界层和内部层。
6. Motion artifact detection and correction in functional near-infrared spectroscopy: a new hybrid method based on spline interpolation method and Savitzky–Golay filtering [O] . Sahar Jahani, Seyed K. Setarehdan, David A. Boas, 2018

机译：功能近红外光谱中的运动伪影检测和校正：基于样条插值方法和Savitzky-Golay滤波的新混合方法
7. On interpolation of functions with a boundary layer by cubic splines [O] . Igor A. Blatov, Elena V. Kitaeva, Alexander I. Zadorin 2016

机译：在立方样条曲率下与边界层的插值时
8. Cardinal Interpolation and Spline Functions V. The B-Splines for Cardinal Hermite Interpolation [R] . Schoenberg, I. J., Sharma, A. 1971

机译：基数插值和样条函数V.基数Hermite插值的B样条

Parabolic spline interpolation for functions with large gradient in the boundary layer

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