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>