Re: NDSolve and time-delayed equations?

*To*: mathgroup at smc.vnet.net*Subject*: [mg46758] Re: NDSolve and time-delayed equations?*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sun, 7 Mar 2004 01:33:36 -0500 (EST)*Organization*: Universitaet Leipzig*References*: <c298pc$564$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de*Sender*: owner-wri-mathgroup at wolfram.com

Hi, Mathematica can not do this. You need a continuos output Runge-Kutta method that can construct an interpolation function of the solution while the solution is computed. With Mathematica 5 you can try to define your own method and implement the algorithm. And a Google search with http://www.google.de/search?q=%22continuous+output%22+Runge-Kutta&ie=UTF-8&oe=UTF-8&hl=de&btnG=Google+Suche&meta= should help you. Regards Jens 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? > > Gareth Russell > Columbia University