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

• To: mathgroup at smc.vnet.net
• Subject: [mg29085] Re: Why can't Nsolve find a solution to this ?
• From: David Kirkby <REMOOVE_THIS_drkirkby at AND_THIS_ntlworld.com>
• Date: Sun, 27 May 2001 18:04:50 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```   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.

--
Dr. David Kirkby Ph.D,
email: REMOOVE_THIS_drkirkby at AND_THIS_ntlworld.com
former email address: davek at DELLETE_THIS_medphys.ucl.ac.uk
web page: http://www.david-kirkby.co.uk