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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 2, Pages 221–233 (Mi zvmmf4821)  

This article is cited in 17 scientific papers (total in 17 papers)

Spline interpolation on a uniform grid for a function with a boundary layer component

A. I. Zadorina, N. A. Zadorinb

a Omsk Branch of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099 Russia
b Omsk State University, pr. Mira 55a, Omsk, 644077 Russia

Abstract: Spline interpolation of functions of one variable with a boundary-layer component is examined. Functions of this type can arise in the solution of a singularly perturbed boundary value problem on an interval. Spline interpolation formulas that are exact for the boundary-layer component are constructed, and their errors are estimated. Formulas for calculating the derivative based on the constructed interpolants are obtained. Numerical results are presented.

Key words: interpolation of functions of one variable with a boundary-layer component, spline interpolation, large gradients, interpolation error estimate, singularly perturbed boundary value problem.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:2, 211–223

Bibliographic databases:

UDC: 519.63
Received: 24.06.2009

Citation: A. I. Zadorin, N. A. Zadorin, “Spline interpolation on a uniform grid for a function with a boundary layer component”, Zh. Vychisl. Mat. Mat. Fiz., 50:2 (2010), 221–233; Comput. Math. Math. Phys., 50:2 (2010), 211–223

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. A. I. Zadorin, N. A. Zadorin, “Quadrature formulas for functions with a boundary-layer component”, Comput. Math. Math. Phys., 51:11 (2011), 1837–1846  mathnet  crossref  mathscinet  isi
    3. A. I. Zadorin, N. A. Zadorin, “Kvadraturnaya formula Eilera dlya funktsii s pogransloinoi sostavlyayuschei na kusochno-ravnomernoi setke”, Sib. elektron. matem. izv., 10 (2013), 491–503  mathnet
    4. A. I. Zadorin, N. A. Zadorin, “An analogue of Newton–Cotes formula with four nodes for a function with a boundary-layer component”, Num. Anal. Appl., 6:4 (2013), 268–278  mathnet  crossref  mathscinet  elib
    5. A. I. Zadorin, “Cubature formulas for a two-variable function with boundary-layer components”, Comput. Math. Math. Phys., 53:12 (2013), 1808–1818  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. A. I. Zadorin, “Modification of the Euler quadrature formula for functions with a boundary-layer component”, Comput. Math. Math. Phys., 54:10 (2014), 1489–1498  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. A. I. Zadorin, “Interpolyatsiya funktsii dvukh peremennykh s bolshimi gradientami v pogranichnykh sloyakh”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2015, 55–67  mathnet  elib
    8. A. I. Zadorin, “The Lagrange interpolation and the Newton–Cotes formulas for functions with a boundary layer component on piecewise-uniform meshes”, Num. Anal. Appl., 8:3 (2015), 235–247  mathnet  crossref  crossref  mathscinet  elib
    9. 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
    10. Zadorin A., “the Analysis of Lagrange Interpolation For Functions With a Boundary Layer Component”, Finite Difference Methods, Theory and Applications, Lecture Notes in Computer Science, 9045, eds. Dimov I., Farago I., Vulkov L., Springer-Verlag Berlin, 2015, 426–432  crossref  mathscinet  zmath  isi  scopus
    11. A. I. Zadorin, N. A. Zadorin, “Analogue of Newton-Cotes formulas for numerical integration of functions with a boundary-layer component”, Comput. Math. Math. Phys., 56:3 (2016), 358–366  mathnet  crossref  crossref  isi  elib
    12. A. I. Zadorin, “Interpolation formulas for functions with large gradients in the boundary layer and their application”, Model. i analiz inform. sistem, 23:3 (2016), 377–384  mathnet  crossref  mathscinet  elib
    13. Zadorin A.I., “Interpolation of a function of two variables with large gradients in boundary layers”, Lobachevskii J. Math., 37:3 (2016), 349–359  crossref  mathscinet  isi  elib  scopus
    14. A. I. Zadorin, N. A. Zadorin, “Polinomialnaya interpolyatsiya funktsii dvukh peremennykh s bolshimi gradientami v pogranichnykh sloyakh”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 158, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2016, 40–50  mathnet  elib
    15. A. I. Zadorin, “The analysis of numerical differentiation formulas on the Shishkin mesh with of a boundary layer”, Num. Anal. Appl., 11:3 (2018), 193–203  mathnet  crossref  crossref  isi  elib  elib
    16. Zadorin A. Tikhovskaya S., “Formulas of Numerical Differentiation on a Uniform Mesh For Functions With the Exponential Boundary Layer”, Int. J. Numer. Anal. Model., 16:4 (2019), 590–608  mathscinet  isi
    17. I. A. Blatov, N. A. Zadorin, “Interpolyatsiya na setke Bakhvalova pri nalichii eksponentsialnogo pogranichnogo sloya”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 161, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2019, 497–508  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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