Re: Control Function With NDsolve

• To: mathgroup at smc.vnet.net
• Subject: [mg19338] Re: Control Function With NDsolve
• From: Eckhard Hennig <hennig at itwm.uni-kl.de>
• Date: Fri, 20 Aug 1999 23:09:26 -0400
• Organization: ITWM
• References: <7p5dm5\$127@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Don Paddleford schrieb in Nachricht <7p5dm5\$127 at smc.vnet.net>...
>In solving a control type dif eq with NDSolve I have the following
>question. Suppose the eq is of the following simplified form
>
> y'[t]==a*f[y[t]]-b*y[t]
> y[0]==0
>
>How to define f so that it starts at f=1, and changes to f=0 when y
>reaches ymax, and then changes back to f=1 when y reaches ymin, and so
>on in oscilatory fashion?
>

Don,

you can define such a function as follows. Note that it is important to
define the pattern for f such that it applies only to numeric arguments.
Otherwise, f[y[t]] would be evaluated prematurely in In[3].

In[1]:= f[y_Real] :=
If[(y > ymax && fval == 1) || (y < ymin && fval == 0),
fval = 1 - fval,
fval]

In[2]:= ymax = 0.9; ymin = 0.1; a = 1; b = 1;

In[3]:= eqs = {y'[t] == a*f[y[t]] - b*y[t], y[0] == 0};

In[4]:= fval = 1; NDSolve[eqs, y[t], {t, 0, 10}];

In[5]:= y1[t_] = y[t] /. First[%];

In[6]:= Plot[y1[t], {t, 0, 10}, PlotRange->All]

-- Eckhard

-----------------------------------------------------------
Dipl.-Ing. Eckhard Hennig      mailto:hennig at itwm.uni-kl.de
Institut fuer Techno- und Wirtschaftsmathematik e.V. (ITWM)
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