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how make function of solution by NDSolve depending on parameter?

• To: mathgroup at smc.vnet.net
• Subject: [mg75096] how make function of solution by NDSolve depending on parameter?
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 16 Apr 2007 20:20:41 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• Reply-to: murray at math.umass.edu

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

• Follow-Ups:
  • Re: how make function of solution by NDSolve depending on parameter?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: how make function of solution by NDSolve depending on parameter?
    • From: "Chris Chiasson" <chris@chiasson.name>