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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 9, Pages 1673–1684 (Mi zvmmf115)  

This article is cited in 7 scientific papers (total in 7 papers)

Refined-mesh interpolation method for functions with a boundary-layer component

A. I. Zadorin

Omsk Branch of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099, Russia

Abstract: Linear and quadratic spline interpolation methods for a one-variable function with a boundary-layer component are examined. It is shown that the interpolation method for such a function leads to considerable errors when applied on a uniform mesh. The error of linear and quadratic spline interpolations on meshes that are refined in the boundary layer is estimated. Numerical results are presented.

Key words: refined-mesh interpolation methods, function with a boundary-layer component, spline interpolation of functions of one variable.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:9, 1634–1645

Bibliographic databases:

UDC: 519.63
Received: 27.11.2007
Revised: 26.02.2008

Citation: A. I. Zadorin, “Refined-mesh interpolation method for functions with a boundary-layer component”, Zh. Vychisl. Mat. Mat. Fiz., 48:9 (2008), 1673–1684; Comput. Math. Math. Phys., 48:9 (2008), 1634–1645

Citation in format AMSBIB
\by A.~I.~Zadorin
\paper Refined-mesh interpolation method for functions with a~boundary-layer component
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 9
\pages 1673--1684
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 9
\pages 1634--1645

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    This publication is cited in the following articles:
    1. Vulkov L.G., Zadorin A.I., “Two-grid algorithms for an ordinary second order equation with an exponential boundary layer in the solution”, Int. J. Numer. Anal. Model., 7:3 (2010), 580–592  mathscinet  zmath  isi  elib
    2. A. I. Zadorin, N. A. Zadorin, “Spline interpolation on a uniform grid for a function with a boundary layer component”, Comput. Math. Math. Phys., 50:2 (2010), 211–223  mathnet  crossref  mathscinet  adsnasa  isi
    3. A. I. Zadorin, N. A. Zadorin, “Interpolyatsiya funktsii s pogransloinymi sostavlyayuschimi i ee primenenie v dvukhsetochnom metode”, Sib. elektron. matem. izv., 8 (2011), 247–267  mathnet
    4. A. I. Zadorin, S. V. Tikhovskaya, “Solution of second order nonlinear singular perturbation ordinary differential equation based on the Samarskii scheme”, Num. Anal. Appl., 6:1 (2013), 9–23  mathnet  crossref  mathscinet  elib
    5. A. I. Zadorin, S. V. Tikhovskaya, “Dvukhsetochnyi metod dlya nelineinoi singulyarno vozmuschennoi kraevoi zadachi na setke Shishkina”, Sib. zhurn. industr. matem., 16:1 (2013), 42–55  mathnet  mathscinet
    6. Zadorin A.I. Tikhovskaya S.V. Zadorin N.A., “a Two-Grid Method For Elliptic Problem With Boundary Layers”, Appl. Numer. Math., 93:SI (2015), 270–278  crossref  mathscinet  zmath  isi  elib  scopus
    7. Tikhovskaya S.V. Zadorin A.I., “a Two-Grid Method With Richardson Extrapolation For a Semilinear Convection-Diffusion Problem”, Application of Mathematics in Technical and Natural Sciences (Amitans'15), AIP Conference Proceedings, 1684, ed. Todorov M., Amer Inst Physics, 2015, 090007  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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