An iterative method for the multipliers of periodic delay-differential
equations and the analysis of a PDE milling model
O. Rott and E. Jarlebring
Locally convergent iterative schemes have turned out to be very useful
in the analysis of the characteristic roots of delay-differential
equations (DDEs) with constant coefficients. In this work we present a
locally convergent iterative scheme for the characteristic multipliers
of periodic-coefficient DDEs. The method is an adaption of an
iterative method called residual inverse iteration. The possibility to
use this method stems from an observation that the characteristic
matrix can be expressed with the fundamental solution of a
differential equation. We apply the method to a coupled milling model
containing a partial and an ordinary differential equation. The
conclusion of the numerical results is that the stability diagram of
the coupled model differs significantly from the combined stabilty
diagrams for each subsystem.