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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 1, Pages 38–43 (Mi zvmmf4810)  

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

On the general nonlinear selfadjoint spectral problem for systems of ordinary differential equations with singularities

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

a Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moskow, 125047 Russia

Abstract: A nonlinear self-adjoint eigenvalue problem for the general linear system of ordinary differential equations is examined on an unbounded interval. A method is proposed for the approximate reduction of this problem to the corresponding problem on a finite interval. Under the assumption that the initial data are monotone functions of the spectral parameter, a method is given for determining the number of eigenvalues lying on a prescribed interval of this parameter. No direct calculation of eigenvalues is required in this method.

Key words: ordinary differential equation, nonlinear self-adjoint eigenvalue problem, eigenvalues, numerical method for determining the number of eigenvalues.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:1, 32–37

Bibliographic databases:

UDC: 519.62
Received: 19.05.2009

Citation: A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On the general nonlinear selfadjoint spectral problem for systems of ordinary differential equations with singularities”, Zh. Vychisl. Mat. Mat. Fiz., 50:1 (2010), 38–43; Comput. Math. Math. Phys., 50:1 (2010), 32–37

Citation in format AMSBIB
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\paper On the general nonlinear selfadjoint spectral problem for systems of ordinary differential equations with singularities
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\pages 38--43
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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. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On a singular nonlinear self-adjoint spectral problem for differential-algebraic systems of equations”, Comput. Math. Math. Phys., 50:2 (2010), 238–243  mathnet  crossref  mathscinet  adsnasa  isi
    2. M. K. Kerimov, “On the 85th birthday of Aleksandr Aleksandrovich Abramov”, Comput. Math. Math. Phys., 51:10 (2011), 1653–1658  mathnet  crossref  mathscinet  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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