A Jacobi‐Davidson method for two real parameter nonlinear eigenvalue problems arising from delay differential equations

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)