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Re: To plot solutions, FindRoot as a function


"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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