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Re: To plot solutions, FindRoot as a function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg37372] Re: To plot solutions, FindRoot as a function
*From*: "Peltio" <peltio at twilight.zone>
*Date*: Fri, 25 Oct 2002 02:48:23 -0400 (EDT)
*Organization*: Peltio Inc.
*References*: <ap861r$53e$1@smc.vnet.net>
*Reply-to*: "Peltio" <peltioNOSP at Miname.com.invalid>
*Sender*: owner-wri-mathgroup at wolfram.com
"Veniamin Abalmassov" wrote:
>I'd like to plot the solution of an equation which depends on two
>parameters, e.g.
>sol[a_,b_]:=FindRoot[a*Tanh[b*x] == x, {x, {0.01, 0.1}}]
>Plot[sol[a,b], {a, 1, 2}, {b, 1, 2}]
You were almost there!
The problem is the typo (Plot instead of Plot3D) and the fact that FindRoot,
and hence sol, returns a replacement rule instead of the value of x.
You will be better off with:
sol[a_,b_]:=x /. FindRoot[a*Tanh[b*x] == x, {x, {0.01, 0.1}}]
Plot3D[sol[a,b], {a, 1, 2}, {b, 1, 2}]
And if you want to see the single points (here I use a grid with a spacing
of 0.05 units) you can use this, instead:
sol[a_,b_]:=FindRoot[a*Tanh[b*x]==x,{x,{0.01,0.1}}]
vals=Flatten[Table[{a,b,x/.sol[a,b]},{a,1,2,.05},{b,1,2,.05}],1];
pts=Point/@vals;
Show[Graphics3D[pts],BoxRatios\[Rule]{1,1,1},Axes\[Rule]True]
cheers,
Peltio
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