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MathGroup Archive 2008

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Help with find root needed

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88910] Help with find root needed
  • From: Aaron Fude <aaronfude at gmail.com>
  • Date: Wed, 21 May 2008 14:49:06 -0400 (EDT)

Hi,

In what follows, I'm looking for the largest root of a function, that
is also a function of two parameters. The Manipulate command shows me
that the root is consistently there (albeit near a singularity which
might be what's causing problems). However, FindRoot doesn't find it
as the plot shows. I get one error, but my guess is that it's
referring to one particular point on the plot.

f[z_, h_, \[Gamma]_] :=
  Tanh[h*z] + (\[Gamma]^2 + 1 - z^2)/(\[Gamma]^2 - 1 - z^2) *
    z/\[Gamma];
Manipulate[
 Plot[f[z, h, \[Gamma]], {z, 0, 10}], {h, .1, 10}, {\[Gamma], .1,
  10}]
K[h_, \[Gamma]_] :=
  z /. FindRoot[f[z, h, \[Gamma]] == 0, {z, 10, 1, 10}];
Plot3D[K[h, \[Gamma]], {h, .1, 10}, {\[Gamma], .1, 10}]

Many thanks in advance!

Aaron


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