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Re: Using "If" and "NDSolve" together

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106842] Re: [mg106781] Using "If" and "NDSolve" together
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Sun, 24 Jan 2010 05:45:45 -0500 (EST)
  • References: <201001231233.HAA16276@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

Oh, what a tangled web you weave.

Clear[funcao]
funcao[first_, last_] :=
  Module[{k0 = 10^-2, k1 = 10^-5, k2 = 10^-6, k3 = 10, a, b, c},
   a = a /. First@
      NDSolve[{a'[t] == k0 Boole[first <= t <= last] - k1 a[t],
        b'[t] == k1 a[t] - k2 b[t], c'[t] == k2 b[t] - k3 c[t],
        a[0] == 2 10^-6, b[0] == 0, c[0] == 0}, {a, b, c}, {t, 0,
        1000}];
   Plot[a@t, {t, 0, 1000}, PlotRange -> All]
   ]
funcao[0, 100]
funcao[0, 900]
funcao[100, 900]

Bobby

On Sat, 23 Jan 2010 06:33:50 -0600, Benfeitas <rui.benfeitas at gmail.com>  
wrote:

> Hello!
>
> I have a tricky job to do: I want to simulate something, and want to
> assign a value to a variable under certain conditions. Those are, if
> time is within a certain interval, I want that variable to have that
> value. Otherwise, I want it to have other value.
>
> Until now, I have been trying to use the following command:
>
> Funcao[first_, last_] :=
>  Plot[A[t] /.
>    NDSolve[
>           {A'[t] == k0 A0 - k1 A[t], B'[t] == k1 A[t] - k2 B[t],
>           C'[t] == k2 B[t] - k3 C[t], A[0] == 2 10^-6, B[0] == 0,
>           C[0] == 0} /. k0 -> 10^-2 /. k1 -> 10^-5 /. k2 -> 10^-6 /.
>           k3 -> 10^1 /. If[first < t < last, A0 -> 1, 0], {A, B, C},
> {t,
>      0, 1000}], {t, 0, 1000}]
>
>
>
> for some reason, it is not working, and I cannot figure out why...
>
> With that command I will want to plot A[t], for t->{0,1000}, and
> considering that A0->1 if first<t<last, and A0->0 if t<first or
> t>last. That way, A[t] should be higher if first<t<last.
>
> Can you guys please give me some tips? Thanks
>


-- 
DrMajorBob at yahoo.com


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