|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
|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.
|URI:||http://hdl.handle.net/11420/6302||ISSN:||1099-1506||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
|Journal:||Numerical linear algebra with applications|
|Appears in Collections:||Publications without fulltext|
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