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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 9, Pages 1575–1579 (Mi zvmmf594)  

This article is cited in 1 scientific paper (total in 2 paper)

On a method for solving the nonlinear eigenvalue problem for a differential algebraic system of equations

A. A. Abramova, V. I. Ul'yanovaa, L. F. Yukhnob

a Dorodnicyn Computational Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
b Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia

Abstract: For a linear differential algebraic system of equations, a method for determining the number of eigenvalues in a neighborhood of a given complex scalar is proposed and examined. It is assumed that the coefficients of the system and the entries in the matrices of the boundary conditions depend analytically on the spectral parameter. Constructions typical for the argument principle are employed, although the functions arising in the proposed method are not analytic.

Key words: differential algebraic equation, nonlinear eigenvalue problem.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:9, 1520–1524

Bibliographic databases:
UDC: 519.624.2
Received: 21.12.2004

Citation: A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On a method for solving the nonlinear eigenvalue problem for a differential algebraic system of equations”, Zh. Vychisl. Mat. Mat. Fiz., 45:9 (2005), 1575–1579; Comput. Math. Math. Phys., 45:9 (2005), 1520–1524

Citation in format AMSBIB
\Bibitem{AbrUlyYuk05}
\by A.~A.~Abramov, V.~I.~Ul'yanova, L.~F.~Yukhno
\paper On a method for solving the nonlinear eigenvalue problem for a differential algebraic system of equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 9
\pages 1575--1579
\mathnet{http://mi.mathnet.ru/zvmmf594}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2216068}
\zmath{https://zbmath.org/?q=an:1097.34512}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 9
\pages 1520--1524


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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. Abramov A.A., Ul'yanova V.I., Yukhno L.F., “A method for solving boundary value problems and spectral problems for linear differential-algebraic systems”, Differential Equations, 42:7 (2006), 932–940  mathnet  crossref  mathscinet  zmath  isi  scopus
    2. “On the 80th Birthday of Aleksandr Aleksandrovich Abramov”, Comput. Math. Math. Phys., 46:7 (2006), 1081–1085  mathnet  crossref  mathscinet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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