Publisher DOI: 10.1002/nla.1848
Title: A Jacobi-Davidson method for two-real-parameter nonlinear eigenvalue problems arising from delay-differential equations
Language: English
Authors: Meerbergen, Karl 
Schröder, Christian 
Voß, Heinrich 
Keywords: Critical delay; Delay-differential equation; Jacobi-Davidson; Nonlinear eigenvalue problem; Two-parameter eigenvalue problem
Issue Date: 9-Jul-2012
Publisher: Wiley
Source: Numerical Linear Algebra with Applications 5 (20): 852-868 (2013-10-01)
Abstract (english): 
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.
ISSN: 1099-1506
Journal: Numerical linear algebra with applications 
Institute: Mathematik E-10 
Document Type: Article
Project: Interuniversity Attraction Poles Program 
More Funding information: Belgian State Science Policy Office
Research Council K.U. Leuven
MATHEON, the DFG research Center in Berlin
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