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International Workshop on Numerical Analysis and Its Applications

WNAA 1996: Numerical Analysis and Its Applications pp 227–235Cite as

Newton's method for solution of one complex eigenvalue problem

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1196))

Abstract

An eigenvalue problem with complex coefficient is consider in this paper. The mathematical model described the electrohydrodynamic instability of a layer of insulating liquid bounded by one side by rigid electrode and the other side is liquid-liquid interface and subjected to a electric field. Using the continuous analog of Newton's method, a numerical algorithm for solving this problem is developed. The original problem depend of many physical parameters. The numerical exprements show that there exist such value of parameters for which the imaginary part of the eigenvalue with minimal absolute value vanish. It means that the oscillatory modes of instability can occur.

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Authors and Affiliations

  1. Institute of Mathematics, Acad.G.Bontchev Str., Bl.8, 1113, Sofia, Bulgaria

    M. Kaschiev & D. Koulova-Nenova

  2. Institute of Mechanics, Acad.G.Bontchev Str., Bl.4, 1113, Sofia, Bulgaria

    M. Kaschiev & D. Koulova-Nenova

Authors
  1. M. Kaschiev
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  2. D. Koulova-Nenova
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Editor information

Lubin Vulkov Jerzy Waśniewski Plamen Yalamov

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© 1997 Springer-Verlag Berlin Heidelberg

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Kaschiev, M., Koulova-Nenova, D. (1997). Newton's method for solution of one complex eigenvalue problem. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_98

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  • DOI: https://doi.org/10.1007/3-540-62598-4_98

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62598-8

  • Online ISBN: 978-3-540-68326-1

  • eBook Packages: Springer Book Archive

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