ddec

A Matlab suite for stability sharts and other information on linear, periodic ODEs and DDEs.
version 1.0

Documentation:

• Bueler, E., Guide to ddec: Stability of linear, periodic DDEs using the ddec suite, 2005. (134 KB, PDF)
• Bueler, E., Error bounds for approximate eigenvalues of periodic-coefficient linear delay differential equations, SIAM J. Num. Analysis 45 (6), 2510--2536, 2007.
• Bueler, E., Chebyshev collocation for linear, periodic ordinary and delay differential equations: a posteriori estimates, 2004 (arxiv.org/abs/math.NA/0409464).
• Bueler, E., E. A. Butcher, and V. Averina, Reliable stability charts for linear periodic delay differential equations, SIAM CSE05, Orlando, Feb. 2005. (slides; 131 KB, PDF)
• Bueler, E., V. Averina, and E. A. Butcher, “Periodic Linear DDEs: Collocation Approximation to the Monodromy Operator,” SIAM annual meeting,, Portland, OR, July 12-16, 2004.  Slides: Collocation approximation of the monodromy operator for linear, periodic DDEs (341 KB, PDF)

package:

examples of use:

• Butcher, E. A., P. Nindujarla and E. Bueler, Stability of up- and down-milling using a Chebyshev collocation method, proceedings of ASME DETC 2005, September 2005, Long Beach, CA. (547 KB, PDF)
• Averina, K., I. Kolmanovsky, A. Gibson, G. Song and E. Bueler, Analysis and control of delay-dependent behavior of engine air-to-fuel ratio, for submission to the ASME World Congress, Orlando, Florida, November, 2005.
  
• Nindujarla, P., Stability of Milling using the Chebyshev Collocation Method, M.S. Mechanical Engineering Thesis defense, December 2, 2004.