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

*To*: mathgroup at smc.vnet.net*Subject*: [mg75115] Re: [mg75096] how make function of solution by NDSolve depending on parameter?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 18 Apr 2007 04:51:36 -0400 (EDT)*References*: <200704170020.UAA08810@smc.vnet.net>

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. > > -- > 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 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

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