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

• To: mathgroup at smc.vnet.net
• Subject: [mg29098] Re: [mg29085] Re: Why can't Nsolve find a solution to this ?
• From: BobHanlon at aol.com
• Date: Tue, 29 May 2001 02:57:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```?NSolve

"NSolve[lhs==rhs, var] gives a list \
of numerical approximations to the \
roots of a polynomial equation. \
NSolve[{eqn1, eqn2, ... }, {var1, \
var2, ... }] solves a system of \
polynomial equations."*
Button[More\[Ellipsis], ButtonData :>
"NSolve", Active -> True,

Your equations are not polynomials in the unknown variables.  Use FindRoot.

FindRoot[{1.7863852^2== v^2 + u^2, u *Tan[u] == v},{u, 1.},{v, 1.}]

{u -> 0.9860552092989878,
v -> 1.4895862536291804}

Bob Hanlon

In a message dated 2001/5/27 6:22:44 PM,
REMOOVE_THIS_drkirkby at AND_THIS_ntlworld.com writes:

>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:= 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= 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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