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

```

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