Re: FindRoot with parameterized interpolated function from NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg110759] Re: FindRoot with parameterized interpolated function from NDSolve*From*: Peter Pein <petsie at dordos.net>*Date*: Mon, 5 Jul 2010 06:01:52 -0400 (EDT)*References*: <i0pmlc$slv$1@smc.vnet.net>

Am Sun, 4 Jul 2010 10:09:48 +0000 (UTC) schrieb Ulvi Yurtsever <a at b.c>: > I have an interpolated function obtained > as the solution to a system of ODEs via NDSOlve. > The system and the solution depend on a number > of parameters. I then want to plug this function into > FindRoot to find the numerical solution of a system > of equations which depend on both the dependent variable > of the ODEs and the parameters. Mathematica barfs at > the use of parameters as in the following example: > > First, what works as expected: > > > In[135]:= solnn =. > > In[142]:= > solnn[a_] := > NDSolve[{x'[t] == a *y[t], y'[t] == -x[t], x[0] == 1, y[0] == 0}, {x, > y}, {t, 0, Pi}] > > In[144]:= FindRoot[(x /. solnn[1][[1]])[t] - (y /. solnn[1][[1]])[ > t] == 0, {t, 2}] > > Out[144]= {t -> 2.35619} > > > however: > > > FindRoot[{(x /. solnn[a][[1]])[t] - (y /. solnn[a][[1]])[t] == 0, > a - 1 == 0}, {{a, 0}, {t, 2}}] > > > produces, instead of the expected > > {a->1., t->2.355619}, > > lots of error messages to the effect that NDSolve has encountered non- > numerical initial values etc > > Is there any other way to use FindRoot for the purpose I am trying > to use it? > Define an auxilliary function which evaluates iff a _and_ t have got numeric values (I changed solnn a bit for better handling): In[1]:= Clear[solnn,x,y]; solnn[a_?NumericQ] := Block[{t}, First[ NDSolve[{x'[t] == a*y[t], y'[t] == -x[t], x[0]==1, y[0] == 0}, {x, y}, {t, 0, Pi}] ]] In[3]:= FindRoot[x[t] - y[t] == 0 /. solnn[1], {t ,2}] Out[3]= {t->2.35619} In[4]:= target[a_?NumericQ, t_?NumericQ] := x[t] - y[t] /. solnn[a] In[5]:= FindRoot[{target[a, t] == 0, a - t/3 == 0}, {{a, 0}, {t, 2, 0, Pi}}] Out[5]= {a->0.860285,t->2.58085} Peter