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

• To: mathgroup at smc.vnet.net
• Subject: [mg29099] AW: [mg29085] Re: Why can't Nsolve find a solution to this ?
• From: Matthias.Bode at oppenheim.de
• Date: Tue, 29 May 2001 02:57:25 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello David,

I am unable to tell you why NSolve does not find the desired solution but

In[3]:=
FindRoot[ {1.7863852^2 == v^2 + u^2, u Tan[u] == v}, {u, 1}, {v, 1}]

Out[3]=
{u -> 0.986055, v -> 1.48959}

does the trick - numerically.

Best regards,

Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
GERMANY
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 6380
E-mail: matthias.bode at oppenheim.de
Internet: http://www.oppenheim.de

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