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Analogue of Cubic Spline for Functions with Large Gradients in a Boundary Layer

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Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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Abstract

The problem of spline interpolation of functions with large gradients in the boundary layer is studied. It is assumed that the function contains the known up to a factor boundary layer component responsible for the large gradients of this function in the boundary layer. A modification of the cubic spline, based on the fitting to the boundary layer component is proposed. The questions of existence, uniqueness and accuracy of such spline are investigated. Estimates of the interpolation error which are uniform with respect to a small parameter are obtained.

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Acknowledgements

Supported by the program of fundamental scientific researches of the SB RAS 1.1.3., project 0314-2019-0009.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch RAS, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    Alexander Zadorin

  2. Povolzhskiy State University of Telecommunications and Informatics, ul. Lva Tolstogo 23, Samara, 443010, Russia

    Igor’ Blatov

Authors
  1. Alexander Zadorin
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  2. Igor’ Blatov
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Corresponding author

Correspondence to Alexander Zadorin .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Zadorin, A., Blatov, I. (2019). Analogue of Cubic Spline for Functions with Large Gradients in a Boundary Layer. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_77

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_77

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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