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International Conference on Numerical Analysis and Its Applications

NAA 2000: Numerical Analysis and Its Applications pp 451–458Cite as

A Method of Lines Approach to the Numerical Solution of Singularly Perturbed Elliptic Problems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

Abstract

Two elliptic equations with power and interior boundary layers, respectively, in a square are considered. The elliptic problems are reduced to systems of ordinary differential equations by the method of lines. For construction of difference schemes fitted operator technique is used. Uniform convergence for the scheme of the first problem is proved.

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References

  1. Miller J. J. H., O’Riordan E., Shishkin G. I. Fitted numerical methods for singularly perturbed problems. World scientific, Singapure 1996.

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  2. Leveque R., Li Zhilin, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. (1994). 1019–1044.

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  3. Bagaev B. M., Solusenko N. P. Numerical solution for problems with a power boundary layer. Modelling in mechanics, 3, N 2, Novosibirsk, 1989.

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  4. Liseikin V. D. About numerical solution of problems with power boundary layer. Journal of Comput. Math. and Mathem. Physics, 26, N 12, (1986), 1813–1821.

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  5. Zadorin A. I. Numerical solution of a boundary value problem for a system of equations with a small parameter Comput. Math. and Math. Physics, 38, 1998, N8, 1201–1211.

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Rousse, Bulgaria

    J. D. Kandilarov & L. G. Vulkov

  2. Russian Academy of Sciences, Siberian branch, Institute of Mathematics, 644099, Omsk, Russia

    A. I. Zadorin

Authors
  1. J. D. Kandilarov
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  2. L. G. Vulkov
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  3. A. I. Zadorin
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Kandilarov, J.D., Vulkov, L.G., Zadorin, A.I. (2001). A Method of Lines Approach to the Numerical Solution of Singularly Perturbed Elliptic Problems. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_52

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  • DOI: https://doi.org/10.1007/3-540-45262-1_52

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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