| Roots of characteristic equation (smart root-finding) [message #10138] |
Wed, 15 October 1997 00:00 |
Marty Ryba
Messages: 16
Registered: May 1996
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Junior Member |
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Hello,
I wonder if anyone has any routines/suggestions for my problem:
I am trying to examine the stability of a linear oscillator with time
lag, which therefore has a nonlinear characteristic equation (there are
exponentials exp(-lambda*tau) in it). As you may know, the roots of the
characteristic equation correspond to solutions of the differential
equation, and therefore the value of these roots are very important for
assessing stability, etc. Anyway, I'm trying to evaluate stability
(whether the real part of the root is positive or negative) for a wide
range of parameters of the system (computing a bunch of roots and
plotting the contour between positive and negative real components).
I've been using the routine FX_ROOT but I'm having problems in that it
doesn't reliably find the maximal root (the one with the most positive
real component). It happily finds any old root, sensitively dependent
on the location of the initial guesses. I could conceivably take the
complex equation and convert it into a pair of equations and use AMOEBA,
NEWTON, or BROYDEN, but I still have the problem of needing "good"
guesses; I could perform a coarse grid search first, but the equations
are very sensitive to changes in the imaginary component of the root, so
the grid would need to be rather fine and I would need to intelligently
find the local minimum of the magnitude with the most positive real
compenent.
Any tips/suggestions?
--
Dr. Marty Ryba | Of course nothing I say here is official
MIT Lincoln Laboratory | policy, and Laboratory affililaton is
ryba@ll.mit.edu | for identification purposes only,
| blah, blah, blah, ...
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