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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
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