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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg29091] Re: [mg29085] Re: Why can't Nsolve find a solution to this ?
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Tue, 29 May 2001 02:57:19 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Yes, you are certainly missing something here.
NSolve like solve is primarily intended for solving algebraic equations. In
yoour case what you need is FindRoot.

In[1]:=
 FindRoot[{1.7863852^2== u^2  + v^2 , u Tan[u] == v}, {u,1},{v,1}]
Out[1]=
{u -> 0.986055, v -> 1.48959}


-- 
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/~andrzej/



on 01.5.28 7:04 AM, David Kirkby at
REMOOVE_THIS_drkirkby at AND_THIS_ntlworld.com wrote:

> 
> 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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