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

*To*: mathgroup at smc.vnet.net*Subject*: [mg75164] Re: how make function of solution by NDSolve depending on parameter?*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Thu, 19 Apr 2007 04:29:29 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <f014kb$94o$1@smc.vnet.net> <4625C034.1000801@metrohm.ch>*Reply-to*: murray at math.umass.edu

This response nicely explains the difficulty. I thank all respondents to my query. Your replies have been most helpful. dh wrote: > Hi Murray, > NMinimize does not have the attribute HoldFirst. Therefore, the argument > is evaluated before beeing fed to NMinimize. But at this time k does not > have a value. Therefore, put the first argument into a function that is > evaluated only for numerical values. E.g.: > soln[k_]:=NDSolve[{y'[t]==(k y[t]+Exp[-t])/(1+y[t]),y[0]==1}, > y[t],{t,0,1}]; > fun[k_/;NumberQ[k]]:=y[t]/.soln[k][[1,1]]/.t->0.5; > NMinimize[fun[k],{k,0.1,1}] > hope this helps, Daniel > > > Murray Eisenberg 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 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