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MathGroup Archive 2003

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NDelayDSolve, Dynapac, and delayed dif eqs

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39417] NDelayDSolve, Dynapac, and delayed dif eqs
  • From: "Curt Fischer" <crf3 at po.cwru.edu>
  • Date: Fri, 14 Feb 2003 03:23:35 -0500 (EST)
  • Organization: Case Western Reserve University, Cleveland, OH, USA
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Group:

I am studying a second order system of autonomous, nonlinear, delayed
differential equations.  So far I've used both NDelayDSolve, a package
by Allan Hayes, and Dynpac, a pseudo-package by Al Clark to simulate my
equaitons.

Both did the job, but NDelayDSolve gives me warnings like

FunctionInterpolation::"ncvb":
    "FunctionInterpolation failed to meet the prescribed accuracy and \
precision goals after \!\(6\) recursive bisections near \!\(t\) =
\!\(0\). \
Continuing to refine elsewhere."

every time I run it.  In my system, the two time-dependent variables
take on values between 0 and up to about 10^12 or so, and my initial
function is very far from any equilibrium, so the initial response of
the system is very strong.  Anyway, with one set of parameter values,
the solution that NDelayDSolve gave me coincided with dynpack (despite
the warnings), and wtih another, there were sharp discontinuities in the
solution produced by NDelayDSolve, but not in Dynpac.  I tried changing
the InterpolationOrder, StartingStepSize, and MaxSteps of my
NDelayDSolve function call, but to no avail.  What else can I try to
eliminate these warnings?

Also, as a next step I would like to do stability analysis of the
equilibrium points of my system, as a function of one the parameters.  I
don't know much about this.  Is there a way to test for, eg., Liapunov
stability of delayed diff eqs with Mathematica that isn't too difficult?

--
Curt Fischer
Dept. of Bioengineering, Tokyo Inst. of Tech.





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