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Re: solution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg118289] Re: solution
  • From: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>
  • Date: Wed, 20 Apr 2011 04:28:34 -0400 (EDT)

Hi Amelia

Plot[ (BesselJ[0, x] + 6. x BesselJ[1, x]), {x, -5, 105}]

Shows that there are around 33 roots in (-5, 105).

After executing your (slightly modified) code

r := Table[ k /. FindRoot[BesselJ[0, k] + k BesselJ[1, k] == 0, {k, n},
 WorkingPrecision -> 20], {n, 1, 100}]

checking the results via

roots = Union[r, SameTest -> (Abs[#1 - #2] < 10^-10 &)]
roots // Length

gives a list of 33 roots.

Map[ (BesselJ[0, #] + # BesselJ[1, #] &), roots  ]

confirms them.

With your code, 100 different starting points gives 100 results, but
there appear to be only 33 unique roots in the interval of interest.

Map[ (#[[2]] - #[[1]] &), Partition[ roots, 2, 1 ] ]

throws some light on your conjecture * I think that "step" "n" tend
to Pi*.

Cheers

Barrie



>>> On 19/04/2011 at 8:56 pm, in message
<201104191056.GAA18596 at smc.vnet.net>,
amelia Jackson <meli.jacson at gmail.com> wrote:
> Dear MathGroup,
> 
> I have a problem. I want to find solution:
> r := Table[
> k /. FindRoot[BesselJ[0, k] + k BesselJ[1, k] == 0, {k, n}], {n, 1,
100}]
> 
> but I get about 3o roots. I need about 100 or more.
> I think that "step" "n" tend to Pi
> 
> Please for help...


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