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>
• 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.

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

```

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