Nonlinear eigenvalue problem for a system of ordinary differential equations subject to a nonlocal condition

For a system of linear ordinary differential equations supplemented with a nonlocal condition specified by the Stieltjes integral, the problem of calculating the eigenvalues belonging to a given bounded domain in the complex plane is examined. It is assumed that the coefficient matrix of the system...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 52; no. 2; pp. 213 - 218
Main Authors: Abramov, A. A., Yukhno, L. F.
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01.02.2012
Springer Nature B.V
Subjects:
Boundary conditions
Boundary value problems
Cauchy problems
Computational mathematics
Computational Mathematics and Numerical Analysis
Differential equations
Eigenfunctions
Eigenvalues
Equality
Integrals
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear equations
Numerical analysis
Ordinary differential equations
Spectra
Stieltjes integral
Studies
Stieltjes integral
system of linear ordinary differential equations
nonlocal condition
numerical computation of eigenvalues and eigenfunctions
nonlinear eigenvalue problem
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:For a system of linear ordinary differential equations supplemented with a nonlocal condition specified by the Stieltjes integral, the problem of calculating the eigenvalues belonging to a given bounded domain in the complex plane is examined. It is assumed that the coefficient matrix of the system and the matrix function in the Stieltjes integral are analytic functions of the spectral parameter. A numerically stable method for solving this problem is proposed and justified. It is based on the use of an auxiliary boundary value problem and formulas of the argument principle type. The problem of calculating the corresponding eigenfunctions is also treated.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542512020029