• To: mathgroup at smc.vnet.net
• Subject: [mg3716] Q about Nonlinear Simul. Eq
• From: Jinchul Park <jinchulp at usc.edu>
• Date: Wed, 10 Apr 1996 02:12:57 -0400
• Organization: University of Southern California, Los Angeles, CA
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

I'm a newbie in this group.  I have a question about solving nonlinear
simultaneous equation.  Please forgive me if my question is trivial.

Is there any built-in function solving nonlinear simultaneous equations
in Mathematica?  Or do I have to make a subroutine or a function to do
that?

Currently I'm using Mathematica v. 2.2.3 under UNIX.

The following shows a small example for your reference:

I tried to estimate x and y from this equation:
*********************************************************************
NSolve[{
x - 4 (Exp[-1 - 2x] / (Exp[-1 - 2x] + Exp[-2 - y])) == 0,
y - 4 (Exp[-2 -  y] / (Exp[-1 - 2x] + Exp[-2 - y])) == 0,
x + y                                               == 4
},
{x, y}]
*********************************************************************

After hitting shift+enter, what I get is the following message and the
output:

*********************************************************************
Solve::tdep:
The equations appear to involve transcendental functions of
the variables in an essentially non-algebraic way.

Out[1]=
-1 - 2 x
-4 E
NSolve[{------------------- + x == 0,
-1 - 2 x    -2 - y
E         + E

-2 - y
-4 E
------------------- + y == 0, x + y == 4}, {x, y}]
-1 - 2 x    -2 - y
E         + E
********************************************************************