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MathGroup Archive 2001

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Re: AW: Re: Why can't Nsolve find a solution to this ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg29108] Re: AW: Re: Why can't Nsolve find a solution to this ?
  • From: "Kevin J. McCann" <KevinMcCann at home.com>
  • Date: Wed, 30 May 2001 05:50:23 -0400 (EDT)
  • References: <9evi10$ol5@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

NSolve is for the roots of  polynomial equations, the second equation in 
the set is not.

Kevin

The wise words of Matthias.Bode at oppenheim.de on Tuesday 29 May 2001 03:10:

> 
>    I'd like if possible to obtain an analytical solution to the
> following two simultaneous equations, but given that is apparently not
> likely to be found, I thought of a using NSolve to get a numerical one.
> However, Nsolve can't seem to find a solution, despite the fact that if
> I  write a computer programme in 5 minutes or less to solve it
> numerically. Am I missing something here ??
> 
> The equations arrise from optical waveguides:
> W^2=u^2 + v^2
> v=u tan(u)
> 
> W is known in advance, so I want to find the 2 variables u and v using
> the above 2 equations. I've tried:
> 
> In[2]:= NSolve[ {1.7863852^2== v^2 + u^2, u Tan[u] == v},{u,v}]
> 
> Solve::tdep: The equations appear to involve the variables to be solved
> for in
>     an essentially non-algebraic way.
> 
>                             2    2
> Out[2]= NSolve[{3.19117 == u  + v , u Tan[u] == v}, {u, v}]
> 
> Yet I know there is a solution to this : u->0.986, v->1.4893.
> 
> Any suggestions on how to get Mathematica to find such solutions ???
> 
> I'm using Mathematica 4.01 on a Sun SPARCstation 20, with Solaris 8.
> 


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