Re: FindRoot with parameterized interpolated function

*To*: mathgroup at smc.vnet.net*Subject*: [mg110758] Re: FindRoot with parameterized interpolated function*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Mon, 5 Jul 2010 06:01:40 -0400 (EDT)

solnn[a_?NumericQ] := NDSolve[{ x'[tt] == a*y[tt], y'[tt] == -x[tt], x[0] == 1, y[0] == 0}, {x, y}, {tt, 0, Pi}][[1]] FindRoot[ (x /. solnn[1])[t] - (y /. solnn[1])[t] == 0, {t, 2}] {t->2.35619} f[a_?NumericQ, t_?NumericQ] := (x /. solnn[a])[t] - (y /. solnn[a])[t] Plot3D[f[a, t], {a, 0, 2}, {t, 0, Pi}] With[{a = 2 RandomReal[]}, {a, t /. FindRoot[f[a, t] == 0, {t, Pi/2}][[1]]}] {1.01545,2.3344} f @@ % 0. FindRoot[{f[a, t] == 0, a - 1 == 0}, {{a, 1}, {t, Pi/2}}] {a->1.,t->2.35619} f[a, t] /. % -3.33067*10^-16 Bob Hanlon ---- Ulvi Yurtsever <a at b.c> wrote: ============= 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?