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MathGroup Archive 2004

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Re: solving nonlinear equation with mathematica !!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47155] Re: solving nonlinear equation with mathematica !!
  • From: bobhanlon at aol.com (Bob Hanlon)
  • Date: Sun, 28 Mar 2004 00:07:45 -0500 (EST)
  • References: <c438oj$ekr$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Check your graph; you must have a wrong equation.

Needs["Graphics`ImplicitPlot`"];

Needs["Graphics`Colors`"];

eqns={x^2-y-1==0, 10*x*Exp[-x]-y==0};

FindRoot[eqns, 
      {x,#[[1]]}, {y,#[[2]]}]& /@ 
  {{-0.1, -1}, {2, 2.5}}

{{x -> -0.09058966837961079, y -> -0.9917935119828722}, 
  {x -> 1.9446329780681595, y -> 2.7815974193902346}}

pts = {x, y} /. %;

ImplicitPlot[eqns,{x,-0.2,2.2}, 
    AspectRatio->1/GoldenRatio, 
    Frame->True, Axes->False,
    PlotStyle -> {Blue, Green},
    Epilog-> {AbsolutePointSize[4], Red, Point /@ pts}];

Plot[{x^2-1, 10*x*Exp[-x]}, {x,-0.2,2.2}, 
    Frame->True, Axes->False,
    PlotStyle -> {Blue, Green},
    Epilog-> {AbsolutePointSize[4], Red, Point /@ pts}];


Bob Hanlon

In article <c438oj$ekr$1 at smc.vnet.net>, m004202002 at yahoo.com (why) wrote:

<< I face root finding problem solving nonlinear equation

I have system nonlinear equation

x^2-y-1 = 0;
10x exp(-x)-y = 0 ;

If you draw the graph you see two intersecting point .

I have found a point [Using FindRoot function ]
In (-0.1,-0.5) the point is (-0.0905897,-0.991794 )---it is OK 

But 
In (2.0,1.0) the point is (1.94463,2.7816)
But the graph says the x->2.something ,y->1.somthing 
I have used same FindRoot function to find the root
in (2.0,1.0 ).


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