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A Jacobi‐Davidson method for two real parameter nonlinear eigenvalue problems arising from delay differential equations
Author(s) -
Meerbergen Karl,
Schröder Christian,
Voss Heinrich
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110438
Subject(s) - solver , eigenvalues and eigenvectors , nonlinear system , mathematics , differential equation , scale (ratio) , jacobi method , mathematical analysis , mathematical optimization , physics , quantum mechanics
The critical delays of a delay‐differential equation can be computed by solving a nonlinear two‐parameter eigenvalue problem. For large scale problems, we propose new correction equations for a Jacobi‐Davidson type method, that also forces real valued critical delays. We present two different equations: 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. A numerical example of a large scale problem arising from PDEs shows the effectiveness of the method. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)