Re: how make function of solution by NDSolve depending on parameter?

• To: mathgroup at smc.vnet.net
• Subject: [mg75144] Re: how make function of solution by NDSolve depending on parameter?
• From: dh <dh at metrohm.ch>
• Date: Wed, 18 Apr 2007 05:06:28 -0400 (EDT)
• References: <f014kb\$94o\$1@smc.vnet.net>

```
Hi Murray,

NMinimize does not have the attribute HoldFirst. Therefore, the argument

is evaluated before beeing fed to NMinimize. But at this time k does not

have a value. Therefore, put the first argument into a function that is

evaluated only for numerical values. E.g.:

soln[k_]:=NDSolve[{y'[t]==(k y[t]+Exp[-t])/(1+y[t]),y[0]==1}, y[t],{t,0,1}];

fun[k_/;NumberQ[k]]:=y[t]/.soln[k][[1,1]]/.t->0.5;

NMinimize[fun[k],{k,0.1,1}]

hope this helps, Daniel

Murray Eisenberg wrote:

> I have an initial-value problem that depends upon a parameter k.  I want

> to feed the result from NDSolve for it into a function of k and then

> operate upon that function, say to find a minimum with respect to k.

>

> As a toy example:

>

>    soln[k_]:=NDSolve[{y'[t] ==(k y[t]+Exp[-t])/(1+y[t]),

>                y[0]==1},y[t],{t,0,1}]

>

> I want to do something like this:

>

>    NMinimize[Evaluate[y[t] /. soln[k]] /. t -> 0.5, {k, 0.1, 1}]

>

> That generates errors about non-numerical values.  Yet I can get a

> result from, for example:

>

>   Table[Evaluate[y[t] /. soln[k]] /. t -> 0.5, {k, 0, 1}]

>

> So how can I create the function of k I want to feed into NMinimize?  I

> presume the issue is when NDSolve gets called, but I'm not sure how to

> resolve this issue.

>

```

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