Re: Debug of FindRoot
- To: mathgroup at smc.vnet.net
- Subject: [mg78915] Re: Debug of FindRoot
- From: dh <dh at metrohm.ch>
- Date: Thu, 12 Jul 2007 05:28:28 -0400 (EDT)
- References: <f72c9h$d75$1@smc.vnet.net>
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.
>
>