Re: NDSolve and time-delayed equations?

*To*: mathgroup at smc.vnet.net*Subject*: [mg46895] Re: [mg46750] NDSolve and time-delayed equations?*From*: sean kim <sean_incali at yahoo.com>*Date*: Sun, 14 Mar 2004 03:24:14 -0500 (EST)*Reply-to*: sean_incali01 at yahoo.com*Sender*: owner-wri-mathgroup at wolfram.com

the equation you posted is solvable in Mathematica 5.0 and i'm not sure if it's delay equation. like... Plot[Evaluate[ n[t] /. NDSolve[{n'[t] == 0.5*n[t]*(1 - n[t]/100), n[0] == 10}, n, {t, 0, 20}] ], {t, 0, 10}] the one with [t, t-lag] is a delay equation though. what kind of problem results in an equation as the first? would you mind explain it? sean --- Gareth Russell <gjr2008 at columbia.edu> 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 > __________________________________ Do you Yahoo!? Yahoo! Mail - More reliable, more storage, less spam http://mail.yahoo.com