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.