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Sib. Zh. Vychisl. Mat., 2007, Volume 10, Number 3, Pages 267–275 (Mi sjvm83)  

This article is cited in 22 scientific papers (total in 22 papers)

Method of interpolation for a boundary layer problem

A. I. Zadorin

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science

Abstract: A singularly perturbed boundary value problem for a second order ordinary differential equation is considered. It is assumed that the solution is found at the nodes of a uniform or nonuniform mesh. An interpolation method taking into account the boundary layer part of the solution is proposed. Using the constructed interpolation function, we find the derivative of the solution with an accuracy uniform with respect to a parameter at any point of the interval.

Key words: ordinary differential equation, boundary layer, mesh solution, linear interpolation, exponential interpolation, numerical differentiation.

Full text: PDF file (193 kB)
References: PDF file   HTML file
UDC: 519.62
Received: 11.04.2006
Revised: 10.10.2006

Citation: A. I. Zadorin, “Method of interpolation for a boundary layer problem”, Sib. Zh. Vychisl. Mat., 10:3 (2007), 267–275

Citation in format AMSBIB
\Bibitem{Zad07}
\by A.~I.~Zadorin
\paper Method of interpolation for a~boundary layer problem
\jour Sib. Zh. Vychisl. Mat.
\yr 2007
\vol 10
\issue 3
\pages 267--275
\mathnet{http://mi.mathnet.ru/sjvm83}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Zadorin, “Refined-mesh interpolation method for functions with a boundary-layer component”, Comput. Math. Math. Phys., 48:9 (2008), 1634–1645  mathnet  crossref  mathscinet  isi
    2. Vulkov L.G., Zadorin A.I., “Two-grid Interpolation Algorithms for Difference Schemes of Exponential Type for Semilinear Diffusion Convection-Dominated Equations”, Applications of Mathematics in Engineering and Economics '34, AIP Conference Proceedings, 1067, 2008, 284–292  crossref  mathscinet  zmath  adsnasa  isi
    3. Vulkov L., Zadorin A.I., “Two-grid Algorithms for The Solution of 2D Semilinear Singularly-perturbed Convection-diffusion Equations Using an Exponential Finite Difference Scheme”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1186, 2009, 371–379  crossref  mathscinet  adsnasa  isi  scopus
    4. Vulkov L.C., Zadorin A.I., “A Two-Grid Algorithm for Solution of the Difference Equations of a System of Singularly Perturbed Semilinear Equations”, Numerical Analysis and its Applications - 4th International Conference, NAA 2008, Lecture Notes in Computer Science, 5434, 2009, 580–587  crossref  mathscinet  zmath  isi
    5. Zadorin A.I., “Interpolation Method for a Function with a Singular Component”, Numerical Analysis and its Applications - 4th International Conference, NAA 2008, Lecture Notes in Computer Science, 5434, 2009, 612–619  crossref  zmath  isi
    6. 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
    7. 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
    8. 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
    9. 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
    10. A. I. Zadorin, N. A. Zadorin, “Interpolation formula for functions with a boundary layer component and its application to derivatives calculation”, Sib. elektron. matem. izv., 9 (2012), 445–455  mathnet
    11. 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
    12. 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
    13. 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
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
    19. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Cubic spline interpolation of functions with high gradients in boundary layers”, Comput. Math. Math. Phys., 57:1 (2017), 7–25  mathnet  crossref  crossref  isi  elib
    20. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer”, Num. Anal. Appl., 10:2 (2017), 108–119  mathnet  crossref  crossref  isi  elib
    21. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Parabolic spline interpolation for functions with large gradient in the boundary layer”, Siberian Math. J., 58:4 (2017), 578–590  mathnet  crossref  crossref  isi  elib  elib
    22. 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
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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