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Re: Using "If" and "NDSolve" together

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  • Subject: [mg106839] Re: [mg106781] Using "If" and "NDSolve" together
  • From: "David Park" <djmpark at>
  • Date: Sun, 24 Jan 2010 05:45:07 -0500 (EST)
  • References: <11235685.1264251844444.JavaMail.root@n11>

Maxim 1: Develop calculations in steps, making sure one step works before
proceeding to the next. And specifically don't nest a complex calculation as
the first argument of a Plot statement!

Maxim 2: Start your variables with small case letters to avoid conflict with
predefined Mathematica symbols.

Step 1. Define your data so that it can be easily used and changed if

(data = {k0 -> 10^-2, k1 -> 10^-5, k2 -> 10^-6, k3 -> 10^1}) // Column  

Step 2. Write a routine to generate your differential equations and check
that it is working properly. Here I use Piecewise as a t function because I
think it will merge with differential equation solving better than an If

Clear[a, b, c]
  last_] := {a'[t] == 
    k0 Piecewise[{{0, t <= first}, {1, first < t < last}, {0, 
         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} /. Data  

deqns[100, 200] // Column  

Step 3. Solve the equations and define the a, b and c functions.

abcsols = First@NDSolve[deqns[100, 200], {a, b, c}, {t, 0, 1000}];
{a[t_], b[t_], c[t_]} = {a[t], b[t], c[t]} /. abcsols

Step 4. Plot the solutions. Here I scaled the functions so they would all
fit on one plot. 

Plot[{a[t], 1000 b[t], 1/2 10^10 c[t]}, {t, 0, 1000},
 Frame -> True,
 Axes -> False]  

So maybe everything is working. The plot could be improved with labeling 

David Park
djmpark at  

From: Benfeitas [mailto:rui.benfeitas at] 


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] /.
          {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},
     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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