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MathGroup Archive 2006

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Re: sorting list of roots af a transcendental function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65278] Re: [mg65260] sorting list of roots af a transcendental function
  • From: "David Park" <djmp at earthlink.net>
  • Date: Thu, 23 Mar 2006 06:58:46 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Try using Ted Ersek's RootSearch from MathSource.

Needs["Ersek`RootSearch`"]
func[a_] := Cot[x] == x/a - a/(4*x)
plotf[a_] := Cot[x] - (x/a - a/(4*x))

RootSearch[func[100], {x, 0.1, 50}]

{{x -> 3.0209}, {x -> 6.04265}, {x -> 9.06603}, {x -> 12.0918}, {x -> 
      15.1206}, {x -> 18.153}, {x -> 21.1895}, {x -> 24.2302}, {x -> 
      27.2756}, {x -> 30.3255}, {x -> 33.3802}, {x -> 36.4395}, {x -> 
      39.5034}, {x -> 42.5716}, {x -> 45.6441}, {x -> 48.7206}}


Plot[plotf[100], {x, 0.1, 50},
  ImageSize -> 500]

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 

From: Dule [mailto:dule23 at gmx.de]
To: mathgroup at smc.vnet.net


Dear group,

for calculating a model i need values for x which are given by the 
transcendental function Cot[x] == x/a - a/(4*x). a is a parameter 0<a<200.
i obtained the roots with Table and FindRoot:
Table[FindRoot[Cot[x] == x/a - a/(4*x), {x, i}], {i, 1, 50}]]

I have two questions:
1. Is there a better way to do this?
2. How can i construct a list, where the values for x, which appear 
multiple are dropped?

Thanks!



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