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Re: Help with find root needed
*To*: mathgroup at smc.vnet.net
*Subject*: [mg88968] Re: [mg88910] Help with find root needed
*From*: "W_Craig Carter" <ccarter at mit.edu>
*Date*: Thu, 22 May 2008 02:39:13 -0400 (EDT)
*References*: <200805211849.OAA10350@smc.vnet.net>
Hello Aaron,
The singularity appears to be only a function of gamma; so its
position can be precalculated. Perhaps, this will work for you:
Kother[h_, \[Gamma]_] :=
z /. Module[{singularity = Re[ Sqrt[\[Gamma]^2 - 1]]},
FindRoot[
f[z, h, \[Gamma]] == 0, {z,
singularity + $MachineEpsilon, $MaxMachineNumber }]]
(*for example*)
Kother[1, 2]
(*returns 2.00483*)
I haven't tested it for the the full range of parameters
On Wed, May 21, 2008 at 2:49 PM, Aaron Fude <aaronfude at gmail.com> wrote:
> 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
>
>
--
W. Craig Carter
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