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FW: Re: To plot solutions, FindRoot as a function
 To: mathgroup at smc.vnet.net
 Subject: [mg37421] FW: [mg37353] Re: To plot solutions, FindRoot as a function
 From: "David Park" <djmp at earthlink.net>
 Date: Sun, 27 Oct 2002 06:33:30 0500 (EST)
 Sender: ownerwrimathgroup at wolfram.com
RE: [mg37353] Re: To plot solutions, FindRoot as a function
Original Message
From: DrBob [mailto:drbob at bigfoot.com]
To: mathgroup at smc.vnet.net
Subject: [mg37421] RE: [mg37353] Re: To plot solutions, FindRoot as a function
I was getting error messages, so I rewrote your solution this way:
Series[a Tanh[b x]  x, {x, 0, 3}] // Normal
x /. Solve[% == 0, x]
start[a_, b_] = Last@%
getSol[a_, b_] := Chop@x /. FindRoot[a Tanh[b x] == x, {x, start[a, b]}]
Table[getSol[a, b], {a, 1, 2, .25}, {b, 1, 2, .25}];
ListDensityPlot[%]
Plot3D[getSol[a, b], {a, 1, 2}, {b, 1, 2}]
Of course, there's also a negative solution:
Series[a Tanh[b x]/x  1, {x, 0, 3}] // Normal
x /. Solve[% == 0, x]
start[a_, b_] = First@%
getSol[a_, b_] := x /. FindRoot[a Tanh[b x] == x, {x, start[a, b]}]
Table[getSol[a, b], {a, 1, 2, .25}, {b, 1, 2, .25}];
ListDensityPlot[%]
Plot3D[getSol[a, b], {a, 1, 2}, {b, 1, 2}]
I tried using the 5th degree series instead, and got nowhere!
DrBob
Original Message
From: Borut L [mailto:gollum at email.si]
To: mathgroup at smc.vnet.net
Subject: [mg37421] [mg37353] Re: To plot solutions, FindRoot as a function
Hi Veniamin,
First, there is always a trivial solution, i.e. x = 0.
You are probably interested in the additional one, yes?. Depending on
the
values of a and b, it exists in Reals or it doesn't.
I would carefully avoid continuous analysis in such problems and looked
for
a discrete solution. You can always increase resolution.
Here we go.
getSol[a_,b_,x_]:=FindRoot[Evaluate[a Tanh[b x] == x],
{x,Sqrt[3 (a b1)/(a b^3)]}]
x/.Table[getSol[a,b,x],{a,1,2,.25},{b,1,2,.25}]
ListDensityPlot[%]
(* continuous :) *)
Plot3D[Evaluate[x/.getSol[a,b,x]],{a,1,2},{b,1,2}]
A note : You should check for the critical a and b, i.e. where the
nontrivial solution vanishes. (e.g. a*b == 1). If you are thinking
where
I've got the initial value for FindRoot, think twice
Series[a Tanh[b x],{x,0,3}]//Normal
Hope that helps,
Borut
"Veniamin Abalmassov" <V.Abalmassov at unibas.ch> wrote in message
news:ap861r$53e$1 at smc.vnet.net...
 Hello,

 I'd like to plot the solution of an equation which depends on two
 parameters, e.g.

 a*Tanh[b*x] == x

 So, I'd like to see it in 3D, one axis is "a", other is "b", and the
last
 is "solution".

 I've tried naively to do it as follows:

 sol[a_,b_]:=FindRoot[a*Tanh[b*x] == x, {x, {0.01, 0.1}}]
 Plot[sol[a,b], {a, 1, 2}, {b, 1, 2}]

 And it doesn't work. Help me, please. What can I do?

 Thanks a lot,

 Veniamin




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