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: Dec-2011
Publisher: Wiley-VCH Verlag
Series Title: Proceedings in Applied Mathematics and Mechanics vol:11 issue:1 pages:915-918
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, i.e. 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, that 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 which is suitable for an iterative linear system solver.
We show numerical examples for large scale problems arising from PDEs.
ISSN: 1617-7061
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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