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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