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MathGroup Archive 2004

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Re: System of DE's

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48187] Re: System of DE's
  • From: "Curt Fischer" <crf3 at po.cwru.edu>
  • Date: Mon, 17 May 2004 03:21:56 -0400 (EDT)
  • References: <c83t0e$mar$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

The built-in Solvers (DSolve, NDSolve, etc.) cannot solve delay differential
equations.  One way to proceed is to download the NDelayDSolve package by
Allan Hayes.  Here's a link to the package download:

http://library.wolfram.com/infocenter/MathSource/725/

This package will solve delay equations numerically.  A difference in this
package (and with delay equations in general) is that you need to specify an
initial function, defined over the entire range of the longest delay.  In
NDelayDSolve, you use pure functions for this.  See the package
documentation for more details.

--
Curt Fischer


Virgil Stokes wrote:
> How can the following system of differential equations be solved in
> Mathematica 5.0.0.0?
> Note, f3 has a delay in it.
>
>      vars = {x[t], y[t], z[t]};
>   k1 = 0.0001; k2 = 0.1;
>   k3 = 0.0001;
>   n = 2000;
>
>   f1 = -k1 x[t] y[t] - k3 x[t] z[t];
>   f2 = -k2 y[t] + k1 x[t] y[t] + k3 x[t] z[t];
>   f3 = k2 (y[t] - y[t - 14]);
>   inits = {x[0] == n - 10, y[0] == 10, z[0] == 0};
>   eqns = {x'[t] == f1, y'[t] == f2, z'[t] == f3};
>
> Thanks,
> --V. Stokes


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