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Topic: solution
Replies: 8   Last Post: Apr 22, 2011 5:10 AM

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Mark McClure

Posts: 193
Registered: 9/12/07
Re: solution
Posted: Apr 21, 2011 2:13 AM
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On Tue, Apr 19, 2011 at 6:56 AM, amelia Jackson <meli.jacson@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




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