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MathGroup Archive 2004

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Re: NDSolve and time-delayed equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46892] Re: NDSolve and time-delayed equations?
  • From: sean_incali at yahoo.com (sean kim)
  • Date: Fri, 12 Mar 2004 23:40:16 -0500 (EST)
  • References: <c298pc$564$1@smc.vnet.net> <c2endi$spa$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

hi.

can you maybe suggest a way to use this package? what are the commands
in this package? i can't seem to get it to work.

maybe some of you can provide some examples using this and other delay
equation packages that's out there. i know paul abbot has written
also....

what is the difference between the two? 


thanks in advance for any inputs.

sean





"Curt Fischer" <crf3 at po.cwru.edu> wrote in message news:<c2endi$spa$1 at smc.vnet.net>...
> Gareth Russell wrote:
> > Hi,
> > 
> > Can NDSolve be used to approximate the dynamics of continuous but
> > time-delayed equations? Here is an example of the standard continuous
> > logistic model used in ecology:
> > 
> > NDSolve[{n'[t] == 0.5*n[t]*(1 - n[t]/100), n[0] == 10}, n, {t, 0, 20}]
> > 
> > It does, of course, have an analytical solution.
> > 
> > A time-delayed version would make the derivative a function of two
> > values: n'[t,t-lag], but I can't figure out if a formulation like this
> > is possible. The key thing seems to be that while the derivative of n
> > is a simple function of two parameters, n itself is not.
> > 
> > Any suggestions, other than iterating as a discrete-time model with
> > very small time-steps?
> 
> Check out the NDelayDSolve package by Allan Hayes.  
> 
> http://library.wolfram.com/infocenter/MathSource/725/
> 
> I've used it to solve delay equations.


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