Title: A Jacobi–Davidson method for two-real-parameter nonlinear eigenvalue problems arising from delay-differential equations
Authors: Meerbergen, Karl ×
Schroeder, Christian
Voss, Heinrich #
Issue Date: Oct-2013
Publisher: John Wiley & Sons, Ltd.
Series Title: Numerical Linear Algebra with Applications vol:20 issue:5 pages:852-868
Abstract: 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.
ISSN: 1070-5325
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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