Re: Debug of FindRoot
- To: mathgroup at smc.vnet.net
- Subject: [mg78946] Re: Debug of FindRoot
- From: Miguel <misvrne at gmail.com>
- Date: Fri, 13 Jul 2007 06:08:04 -0400 (EDT)
- References: <f72c9h$d75$1@smc.vnet.net><f74tei$96s$1@smc.vnet.net>
On 12 jul, 11:49, dh <d... at metrohm.ch> wrote:
> Hi Miguel,
>
> no surprise here. FindRoot with only one start value uses Newton Method.
>
> Look this up and try to understand it (should be not too hard). This
>
> will help you understand why the method goes wrong if the start value is
>
> not close to the root. Further your start values 7 and 10 are on the
>
> wrong side of the discontinuity. With better start values, e.g.: 7.1 and
>
> 10.3 everything works fine.
>
> hope this helps, Daniel
>
>
>
> Miguel wrote:
> > To resolve one of the heat equations it is necesary to calculate the
> > solution of z for BesselJ[0,z]/BesselJ[1,z]==z/Bi, where Bi is the
> > Biot number (equal to 0.5, for example).
>
> > 1.- Plot[{BesselJ[0,z]/BesselJ[1,z],z/Bi},{z,0.001,12}].
>
> >>From this plot I deduce the ranges, more or less, {1,4,7,10}.
>
> > 2.- FindRoot[BesselJ[0,z]/BesselJ[1,z]==z/Bi,{z,#}]&/@{1,4,7,10}
> > {{z->0.940771},{z->3.95937},{z->0.940771},{z->3.95937}}
>
> > I dont understand the reason. With others differents intervals it
> > works fine.- Ocultar texto de la cita -
>
> - Mostrar texto de la cita -
Thanks at all