Re: solution
- To: mathgroup at smc.vnet.net
- Subject: [mg118305] Re: solution
- From: Mark McClure <mcmcclur at unca.edu>
- Date: Thu, 21 Apr 2011 03:10:18 -0400 (EDT)
On Tue, Apr 19, 2011 at 6:56 AM, amelia Jackson <meli.jacson at gmail.com> wrote:
> 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 30 roots. I need about 100 or more.
As others have pointed out, knowledge of the asymptotic behavior of
the roots of the Bessel functions enable a very efficient solution
with FindRoot. Here's an approach using NSolve requiring a little
less sophistication on the part of the user:
z /. NSolve[BesselJ[0, z] + z BesselJ[1, z] == 0 && 0 < z < 315, z]
MM