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Cannot NSolve a system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg88889] Cannot NSolve a system of equations
• From: murat.koyuncu at gmail.com
• Date: Tue, 20 May 2008 06:52:45 -0400 (EDT)

Dear all,

I have the following system that I need to solve, but I cannot get a
sensible result.

Unprotect[In,Out];Clear[In,Out];ClearAll["Global`*"];
zet=0.083;
phi=0.75;eta=1.75;alpha=0.64;y1=0.235457064;y2=0.512465374;y3=0.781779009;
y4=1.109572176; y5=2.360726377;tau1=zet y1^phi;tau2=zet
y2^phi;tau3=zet y3^phi;tau4=zet y4^phi;tau5=zet y5^phi;
 taubar=(tau1 y1+tau2 y2+tau3 y3+tau4 y4+tau5 y5)/
5;a1=(1+phi)tau1;a2=(1+phi)tau2;a3=(1+phi)tau3;a4=(1+phi)tau4;a5=(1+phi)tau5;

eqns1={x1==(roverw(1-tau1)+((roverw+(1-x))y1-1)( (1-taubar+(1-abar)/
eta)x+(taubar-tau1)roverw-(1-taubar)))/(roverw (1-tau1+(1-a1)/eta)-
( (1-taubar+(1-abar)/eta)x+(taubar-tau1)roverw-(1-taubar))),
x2==(roverw(1-tau2)+((roverw+(1-x))y2-1)( (1-taubar+(1-abar)/eta)x+
(taubar-tau2)roverw-(1-taubar)))/(roverw (1-tau2+(1-a2)/eta)-( (1-
taubar+(1-abar)/eta)x+(taubar-tau2)roverw-(1-taubar))),
x3==(roverw(1-tau3)+((roverw+(1-x))y3-1)( (1-taubar+(1-abar)/eta)x+
(taubar-tau3)roverw-(1-taubar)))/(roverw (1-tau3+(1-a3)/eta)-( (1-
taubar+(1-abar)/eta)x+(taubar-tau3)roverw-(1-taubar))),
x4==(roverw(1-tau4)+((roverw+(1-x))y4-1)( (1-taubar+(1-abar)/eta)x+
(taubar-tau4)roverw-(1-taubar)))/(roverw (1-tau4+(1-a4)/eta)-( (1-
taubar+(1-abar)/eta)x+(taubar-tau4)roverw-(1-taubar))),
x5==(roverw(1-tau5)+((roverw+(1-x))y5-1)( (1-taubar+(1-abar)/eta)x+
(taubar-tau5)roverw-(1-taubar)))/(roverw (1-tau5+(1-a5)/eta)-( (1-
taubar+(1-abar)/eta)x+(taubar-tau5)roverw-(1-taubar))),
x==(x1+x2+x3+x4+x5)/5, abar == (a1 x1+a2 x2+a3 x3+a4 x4+a5 x5)/
(5x),roverw==(1-x)(1-alpha)/alpha };

sol=NSolve[eqns1,{x, x1,x2,x3,x4,x5,abar, roverw}];

eqns1 /. sol

Out[741]={{False, False, False, False, False, True, True, True},
{False, False,
   False, False, False, True, True, True}, {False, False, False,
  False, False, True, False, True}, {False, False, True, False, False,
   True, False, True}, {False, False, True, False, False, True, False,
   True}, {False, False, True, True, False, True, True, False}}


What am I doing wrong? Is it just because the system is too
complicated?

Any help would be truly appreciated.
Murat

• Follow-Ups:
  • Re: Cannot NSolve a system of equations
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: Cannot NSolve a system of equations
    • From: Daniel Lichtblau <danl@wolfram.com>