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

**References**:**Help with find root needed***From:*Aaron Fude <aaronfude@gmail.com>