Re: Delay Differential Equations

• To: mathgroup at smc.vnet.net
• Subject: [mg8829] Re: Delay Differential Equations
• From: Mark James <mrj at cs.usyd.edu.au>
• Date: Mon, 29 Sep 1997 02:39:55 -0400
• Organization: Basser Dept of Computer Science, University of Sydney, Australia
• Sender: owner-wri-mathgroup at wolfram.com

```Peter Waterman wrote:
>
> Can I solve DDE of the form
>
> x'(t) = F(t, x(t), x(t-a))
>
> with NDSolve? It appears it is not able to refer back to its own
> solution while it is still in progress.

No it can't.  I have used two solutions to get around this:

1. Modelling the delay as a high-order Bessel-Thomson filter.
Mail me for code.
2. Using a fudge through delay buckets and variable side-effects.
This works reasonably well, though I would only use this if you
were desparate.

It can also be solved in segments equal to the delay time,
using the solution of the previous segment as the delayed
input for the next segment.

--
Mark James                                  |EMAIL : mrj at cs.usyd.edu.au|
Basser Department of Computer Science, F09  |PHONE : +61-2-351-3423    |
The University of Sydney NSW 2006 AUSTRALIA |FAX   : +61-2-351-3838    |
================- WEB: http://www.cs.usyd.edu.au/~mrj -=================

```

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