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