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A Jacobi-Davidson method for two-real-parameter nonlinear eigenvalue problems arising from delay-differential equations
Publikationstyp
Journal Article
Date Issued
2012-07-09
Sprache
English
Author(s)
Institut
TORE-URI
Volume
20
Issue
5
Start Page
852
End Page
868
Citation
Numerical Linear Algebra with Applications 5 (20): 852-868 (2013-10-01)
Publisher DOI
Scopus ID
Publisher
Wiley
The critical delays of a delay-differential equation can be computed by solving a nonlinear two-parameter eigenvalue problem. The solution of this two-parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR-type method for solving such quadratic eigenvalue problem that only computes real-valued critical delays; that is, complex critical delays, which have no physical meaning, are discarded. For large-scale problems, we propose new correction equations for a Newton-type or Jacobi-Davidson style method, which also forces real-valued critical delays. We present three different equations: one real-valued equation using a direct linear system solver, one complex valued equation using a direct linear system solver, and one Jacobi-Davidson style correction equation that is suitable for an iterative linear system solver. We show numerical examples for large-scale problems arising from PDEs. © 2012 John Wiley & Sons, Ltd.
Subjects
Critical delay
Delay-differential equation
Jacobi-Davidson
Nonlinear eigenvalue problem
Two-parameter eigenvalue problem
DDC Class
510: Mathematik