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MathGroup Archive 2007

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75150] Re: how make function of solution by NDSolve depending on parameter?
  • From: jesse.woodroffe at gmail.com
  • Date: Wed, 18 Apr 2007 05:09:33 -0400 (EDT)
  • References: <f014kb$94o$1@smc.vnet.net>

Hi Murray,

One approach would be to replace y[t] with y[t,k] and then minimize
the resulting function w.r.t. k. So for your toy problem, one might
try something like this:

myFunction[t_,k_]=y[t,k]/.NDSolve[{D[y[t,k],t]==(k*y[t,k]+Exp[-t])/
(1+y[t,k]),y[t,k],{t,0,1},{k,0,1}][[1]];
NMinimize[{myFunction[0.5,k],0<=k<=1},k]

Hope that's on the right track.


Jesse Woodroffe


On Apr 16, 7:33 pm, Murray Eisenberg <mur... at math.umass.edu> 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                     mur... 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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