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Sib. Èlektron. Mat. Izv., 2012, Volume 9, Pages 445–455 (Mi semr376)  

This article is cited in 11 scientific papers (total in 11 papers)

Real, complex and functional analysis

Interpolation formula for functions with a boundary layer component and its application to derivatives calculation

A. I. Zadorin, N. A. Zadorin

Omsk department of Sobolev Mathematics Institute SB RAS, Pevtsova 13, 644099, Omsk, Russia

Abstract: An interpolation formula for a function of one variable with a boundary layer component is constructed. Such function corresponds to the solution of a singular perturbed problem. The estimate of an accuracy is obtained. On a base of the constructed interpolation formula the difference formulas for derivatives of the function with a boundary layer component are obtained. Numerical resultes are discussed.

Keywords: function, boundary layer, nonpolynomial interpolation, difference formula for a derivative, accuracy estimation.

Full text: PDF file (448 kB)
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Document Type: Article
UDC: 519.65
MSC: 65D05, 65D25
Received April 9, 2012, published October 17, 2012
Language: English

Citation: A. I. Zadorin, N. A. Zadorin, “Interpolation formula for functions with a boundary layer component and its application to derivatives calculation”, Sib. Èlektron. Mat. Izv., 9 (2012), 445–455

Citation in format AMSBIB
\Bibitem{ZadZad12}
\by A.~I.~Zadorin, N.~A.~Zadorin
\paper Interpolation formula for functions with a boundary layer component and its application to derivatives calculation
\jour Sib. \`Elektron. Mat. Izv.
\yr 2012
\vol 9
\pages 445--455
\mathnet{http://mi.mathnet.ru/semr376}


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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, “Formula Simpsona i ee modifikatsii dlya funktsii s pogransloinoi sostavlyayuschei”, Sib. elektron. matem. izv., 11 (2014), 258–267  mathnet
    2. 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
    3. S. V. Tikhovskaya, “Issledovanie dvukhsetochnogo metoda povyshennoi tochnosti dlya ellipticheskogo uravneniya reaktsii–diffuzii s pogranichnymi sloyami”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2015, 60–74  mathnet  elib
    4. 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
    5. 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
    6. 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
    7. 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
    8. A. I. Zadorin, “Kubaturnye formuly dlya funktsii dvukh peremennykh s bolshimi gradientami v pogranichnykh sloyakh”, Sib. elektron. matem. izv., 14 (2017), 927–936  mathnet  crossref
    9. S. V. Tikhovskaya, “Analysis of the numerical differentiation formulas of functions with large gradients”, Application of Mathematics in Technical and Natural Sciences, AIP Conf. Proc., 1895, ed. M. Todorov, Amer. Inst. Phys., 2017, UNSP 110010-1  crossref  isi  scopus
    10. A. Zadorin, “Two-dimensional interpolation of functions with large gradients in boundary layers”, Numerical Analysis and Its Applications (NAA 2016), Lecture Notes in Computer Science, 10187, ed. I. Dimov, I. Farago, L. Vulkov, Springer, 2017, 760–768  crossref  mathscinet  zmath  isi  scopus
    11. 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
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