       Using "If" and "NDSolve" together

• To: mathgroup at smc.vnet.net
• Subject: [mg106781] Using "If" and "NDSolve" together
• From: Benfeitas <rui.benfeitas at gmail.com>
• Date: Sat, 23 Jan 2010 07:33:50 -0500 (EST)

```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 == 2 10^-6, B == 0,
C == 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

```

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