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The Analysis of Lagrange Interpolation for Functions with a Boundary Layer Component

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9045)

Abstract

Interpolation formulas for the functions of one variable with a boundary layer component are investigated. An interpolated function corresponds to a solution of a singular perturbed problem. An application of Lagrange interpolation on a uniform mesh leads to significant errors. Two approaches for a interpolation of a function with a boundary layer component are considered: a fitting of the interpolation formula to a boundary layer component and the application of Lagrange interpolation on Shishkin mesh. Numerical results are discussed.

Keywords

  • Function
  • Boundary layer
  • Lagrange interpolation
  • Shishkin mesh
  • Nonpolynomial interpolation

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References

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Acknowledgements

Supported by Russian Foundation for Basic Research under Grants 13-01-00618, 15-01-06584.

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Correspondence to Alexander Zadorin .

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Zadorin, A. (2015). The Analysis of Lagrange Interpolation for Functions with a Boundary Layer Component. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science(), vol 9045. Springer, Cham. https://doi.org/10.1007/978-3-319-20239-6_48

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  • DOI: https://doi.org/10.1007/978-3-319-20239-6_48

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20238-9

  • Online ISBN: 978-3-319-20239-6

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