Re: how make function of solution by NDSolve depending

*To*: mathgroup at smc.vnet.net*Subject*: [mg75129] Re: [mg75096] how make function of solution by NDSolve depending*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Wed, 18 Apr 2007 04:58:47 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200704170020.UAA08810@smc.vnet.net> <3679818D-BB41-453E-8F1E-F5A507A55FEA@mimuw.edu.pl>*Reply-to*: murray at math.umass.edu

Actually, according to the Mathematica 5.2 "Advanced Documentation" for NMinimize, I think the syntax I used is OK even though all the examples there show the {var, minvalue, maxvalue} argument itself nested inside a list. But the syntax I used is not correct for the semantics I intended. I really wanted a constraint 0.1<=k<=1 rather than an initial search region, so what I intended was indeed: NMinimize[{Evaluate[y[t] /. soln[k]] /. t -> 0.5, 0.1<=k<=1}, k] That works -- but only after creating the function f as you instructed. Thank you! Andrzej Kozlowski wrote: > > On 17 Apr 2007, at 09:20, 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. > > > The syntax you are trying to use for NMinimize is quite wrong; have you > looked at the documentation: > > ?NMinimize > > You could do this: > > f[k_?NumericQ] := Block[{y}, First[y /. NDSolve[{y'[t] == (k y[t] + > Exp[-t])/(1 + y[t]),y[0] == 1}, y, {t, 0, 1}]]] > > > In[2]:= > NMinimize[{f[k][0.5], 0 <= k <= 1}, k] > > Out[2]= > {1.1879073663327735, {k -> 1.5474783566024743*^-8}} > > > Andrzej Kozlowski > > -- 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

**References**:**how make function of solution by NDSolve depending on parameter?***From:*Murray Eisenberg <murray@math.umass.edu>