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MathGroup Archive 1997

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Re:Solving non-linear equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg6174] Re:[mg6154] Solving non-linear equations
  • From: Ersek_Ted%PAX1A at mr.nawcad.navy.mil
  • Date: Thu, 27 Feb 1997 02:52:21 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Dave Konopnicki  wrote,
>    Hi,
>     I am new to mathematica. I want to find some numeric solutions to a 
system
>      of non-linear equations. I tried to do it with NSolve but I was not 
able
>      to get a solution even with simple systems like:
>      x1==10
>      x2== 10*2^x1
>       I'd like to solve systems like this one:
>       x1==10
>       x2==2^x1
>       x1=f[x2]
>           ...
>         is it possible to do this in mathematica?
>        Thanks
>        -David
>
>          
 -------------------------------------------------------------------------
>
 >        David Konopnicki - konop at cs.technion.ac.il
>
 > 
          
 -------------------------------------------------------------------------

This is a common question.
NSolve will only solve a single polynomial equation.
What you need here is a numerical root finding algorithm.
If it was up to me both commands would be combined into one, and the
program would decide what algorithm is appropriate.

When you are solving two or more non-linear equation, it's
important that you give initial estimates that are in the right ball park.

In the example below I start with estimates  x1= -3,   x2=-2.


In[1]:=   FindRoot[{x2==100/x1, x1-x2^3==0}, {x1, -3}, {x2, -2}]

Out[1]=   {x1->-31.6228,  x2->-3.16228}


FindRoot is one of my favorite features.
Ted Ersek



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