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

*To*: mathgroup at smc.vnet.net*Subject*: [mg75113] Re: [mg75096] how make function of solution by NDSolve depending on parameter?*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Wed, 18 Apr 2007 04:50:35 -0400 (EDT)*References*: <200704170020.UAA08810@smc.vnet.net>

You could try something like this, though there is probably a better approach: In[1]:= soln[k_]:=NDSolve[{y'[t]\[Equal](k y[t]+Exp[-t])/(1+y[t]),y[0]\[Equal]1}, y,{t,0,1}] In[2]:= why[t_,k_?NumberQ]:=y[t]/.soln[k][[1]] In[3]:= NMinimize[why[0.5,k],{k,0.1,1}] Out[3]= \!\({1.148823969616154`*^-13, {k \[Rule] \(-5.281988168180193`*^12\)}}\) On 4/16/07, Murray Eisenberg <murray 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 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 > > -- http://chris.chiasson.name/

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