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

• To: mathgroup at smc.vnet.net
• Subject: [mg75164] Re: how make function of solution by NDSolve depending on parameter?
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Thu, 19 Apr 2007 04:29:29 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <f014kb\$94o\$1@smc.vnet.net> <4625C034.1000801@metrohm.ch>

```This response nicely explains the difficulty.

I thank all respondents to my query. Your replies have been most helpful.

dh wrote:
> 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.
>>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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