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Re: Delay Differential Equations

• To: mathgroup at smc.vnet.net
• Subject: [mg8838] Re: [mg8798] Delay Differential Equations
• From: seanross at worldnet.att.net
• Date: Mon, 29 Sep 1997 02:40:04 -0400
• 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.
> 
> Matthias Weiss
> mweiss at math.niu.edu

This kind of differential equation seems already in the form necessary
for Eulers or Midpoint method.  Why not try one of those?  They are
numerical methods, but you can apply them symbolically too and get
series type answers.  If you are looking for more accuracy than a single
step method, you could use FixedPoint and wait until the value of x[t]
didn't change.  (ie.  FixedPoint[F[t,#,x[t-a]]&,x[t]])