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Re: how make function of solution by NDSolve depending
*To*: mathgroup at smc.vnet.net
*Subject*: [mg75129] Re: [mg75096] how make function of solution by NDSolve depending
*From*: Murray Eisenberg <murray at math.umass.edu>
*Date*: Wed, 18 Apr 2007 04:58:47 -0400 (EDT)
*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst
*References*: <200704170020.UAA08810@smc.vnet.net> <3679818D-BB41-453E-8F1E-F5A507A55FEA@mimuw.edu.pl>
*Reply-to*: murray at math.umass.edu
Actually, according to the Mathematica 5.2 "Advanced Documentation" for
NMinimize, I think the syntax I used is OK even though all the examples
there show the {var, minvalue, maxvalue} argument itself nested inside a
list.
But the syntax I used is not correct for the semantics I intended. I
really wanted a constraint 0.1<=k<=1 rather than an initial search
region, so what I intended was indeed:
NMinimize[{Evaluate[y[t] /. soln[k]] /. t -> 0.5, 0.1<=k<=1}, k]
That works -- but only after creating the function f as you instructed.
Thank you!
Andrzej Kozlowski wrote:
>
> On 17 Apr 2007, at 09:20, 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.
>
>
> The syntax you are trying to use for NMinimize is quite wrong; have you
> looked at the documentation:
>
> ?NMinimize
>
> You could do this:
>
> f[k_?NumericQ] := Block[{y}, First[y /. NDSolve[{y'[t] == (k y[t] +
> Exp[-t])/(1 + y[t]),y[0] == 1}, y, {t, 0, 1}]]]
>
>
> In[2]:=
> NMinimize[{f[k][0.5], 0 <= k <= 1}, k]
>
> Out[2]=
> {1.1879073663327735, {k -> 1.5474783566024743*^-8}}
>
>
> Andrzej Kozlowski
>
>
--
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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