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From: EF on 18 May 2010 01:59

Find Lambda Values for Tan[Lambda] == -([Lambda]/h) and e.g. h = 0.5

the first 10 Lambda Values for h = 0.5 are

In[27]:=Lambda =

Out[27]= {1.837, 4.816, 7.917, 11.04, 14.17, 17.31, 20.44, 23.58, 26.72,
29.86}

My solution requires
1) FindRoot for a wide range of starting (ending) values
2) Eliminate the great number of double real solutions
3) Verify solutions, there are "some" wrong values

Is there a more direct way to the correct lambda values?


E.F.


From: Andrzej Kozlowski on 18 May 2010 06:12
You do not need FindRoot for this. Reduce will find all the solutions in any compact interval. For example, here are all the solutions between -50 and 50.

N[lambda /. {ToRules[Reduce[Tan[lambda] ==== -2*lambda &&
-50 < lambda < 50, lambda]]}, 10]

{-48.70495167,-45.56406660,-42.42328626,-39.28263575,-36.14214890,-33.00187236,-29.86187240,-26.72224637,-23.58314331,-20.44480347,-17.30764054,-14.17243207,-11.04082982,-7.917052685,-4.815842318,-1.836597203,0,1.836597203,4.815842318,7.917052685,11.04082982,14.17243207,17.30764054,20.44480347,23.58314331,26.72224637,29.86187240,33.00187236,36.14214890,39.28263575,42.42328626,45.56406660,48.70495167}

Andrzej Kozlowski


On 18 May 2010, at 15:00, EF wrote:

>
> Find Lambda Values for Tan[Lambda] ==== -([Lambda]/h) and e.g. h == 0.5
>
> the first 10 Lambda Values for h == 0.5 are
>
> In[27]:==Lambda ==
>
> Out[27]== {1.837, 4.816, 7.917, 11.04, 14.17, 17.31, 20.44, 23.58, 26.72,
> 29.86}
>
> My solution requires
> 1) FindRoot for a wide range of starting (ending) values
> 2) Eliminate the great number of double real solutions
> 3) Verify solutions, there are "some" wrong values
>
> Is there a more direct way to the correct lambda values?
>
>
> E.F.
>
>

From: David Park on 19 May 2010 07:03
You might try Ted Ersek's RootSearch package from WRI MathSource. It is much
more convenient than FindRoot for such cases.


David Park
djmpark(a)comcast.net
http://home.comcast.net/~djmpark/



From: EF [mailto:he.frauendorfer(a)t-online.de]


Find Lambda Values for Tan[Lambda] == -([Lambda]/h) and e.g. h = 0.5

the first 10 Lambda Values for h = 0.5 are

In[27]:=Lambda =

Out[27]= {1.837, 4.816, 7.917, 11.04, 14.17, 17.31, 20.44, 23.58, 26.72,
29.86}

My solution requires
1) FindRoot for a wide range of starting (ending) values
2) Eliminate the great number of double real solutions
3) Verify solutions, there are "some" wrong values

Is there a more direct way to the correct lambda values?


E.F.




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