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...