Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.soft-sys.math.mathematica > #1779 > unrolled thread

solution

Back to article view | Back to comp.soft-sys.math.mathematica

Contents

  solution amelia Jackson <meli.jacson@gmail.com> - 2011-04-19 10:56 +0000
    Re: solution "Sjoerd C. de Vries" <sjoerd.c.devries@gmail.com> - 2011-04-20 08:27 +0000
    Re: solution Gary Wardall <gwardall@gmail.com> - 2011-04-20 08:29 +0000
    Re: solution Peter <petsie@dordos.net> - 2011-04-22 09:40 +0000

#1779 — solution

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 30 roots. I need about 100 or more.
I think that "step" "n" tend to Pi

Please for help...

[toc] | [next] | [standalone]

#1790

Why don't you increase the number of starting values?

With 100 the number of unique solutions found by Mathematica is 42 (a
magic number in certain circles). If you take 260 instead you'll get
100 roots.

Cheers -- Sjoerd

Fast responses to Mathematica questions at StackOverflow
http://stackoverflow.com/questions/tagged/mathematica



On Apr 19, 12:56 pm, amelia Jackson <meli.jac...@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, 1=
00}]
>
> but I get about 30 roots. I need about 100 or more.
> I think that "step" "n" tend to Pi
>
> Please for help...

[toc] | [prev] | [next] | [standalone]

#1803

On Apr 19, 5:56 am, amelia Jackson <meli.jac...@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 30 roots. I need about 100 or more.
> I think that "step" "n" tend to Pi
>
> Please for help...

Ameia,


I have no problem creating that table. I don't know how accurate the
table is but my version of Mathematica does produce the table. I am
using 8.0.1.0 on a mac powerbook.

Good Luck

Gary

[toc] | [prev] | [next] | [standalone]

#1834

Am 19.04.2011 12:56, schrieb amelia Jackson:
> 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 30 roots. I need about 100 or more.
> I think that "step" "n" tend to Pi
>
> Please for help...

Hi Amelia,

FindRoot[f[k]==0,{k,kstart,k0,k1}] looks only in the interval [k0,k1] 
for roots. Unfortunately it returns one of the boundaries when no root 
is found. So we have to check if in that case the returned value is a 
root by chance:

f[k_]=BesselJ[0,k]+k BesselJ[1,k];
Length[zeros=Block[{cnt=0,k0=2.,k},
  NestWhileList[
   (k0++;
    (k /. FindRoot[f[k] == 0, {k, k0 + 1/2, k0, k0 + 1}]) /.
      x:(k0 | k0 + 1) /; Chop[f[x]] != 0 :> Unevaluated@Sequence[])&,
   {},
   Length[{##}] <= 100 &, All]
  ] // Rest
] // Quiet

You can check if some roots have been left out using:

Plot[f[x]/Sqrt[x], {x, 3, Last[zeros] + .2}, Mesh -> {zeros}, 
MeshFunctions -> {#1 &}, MeshStyle -> Red, ImageSize -> 1200, 
AspectRatio -> 1/10]

Peter

[toc] | [prev] | [standalone]

Back to top | Article view | comp.soft-sys.math.mathematica

csiph-web