Re: NDSolve and time-delayed equations?

*To*: mathgroup at smc.vnet.net*Subject*: [mg46763] Re: NDSolve and time-delayed equations?*From*: "Curt Fischer" <crf3 at po.cwru.edu>*Date*: Sun, 7 Mar 2004 01:33:41 -0500 (EST)*References*: <c298pc$564$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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. -- Curt Fischer