Re: Cannot NSolve a system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg88932] Re: Cannot NSolve a system of equations
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 21 May 2008 14:53:13 -0400 (EDT)

```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)/(5 x),
roverw == (1 - x) (1 - alpha)/alpha};

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

Select[sol, And @@ (eqns1 /. #) &]

{}

Increasing the working precision helps

Off[NSolve::precw];

sol2 = NSolve[eqns1, {x, x1, x2, x3, x4, x5, abar, roverw},
WorkingPrecision -> 50];

Select[sol2, And @@ (eqns1 /. #) &]

{{x->0.41708623092950157741569019179902289185045201412813,x1->0.\
692440249232143611072102477625080745344157628899,x2->0.\
604422024572264901699315484017555974822809818657,x3->0.\
5127989690938688778766742187652415932939481958373,x4->0.\
39437767611147931754234647185921962409136124978897,x5->-0.\
11860776436224882111198769327198347830001682254199,abar->0.\
08545766887516266300728185720734114355092900559414,roverw->0.\
327888995102155362703674267113049623334120742053},{x->1.\
0000000000000000000000000000000000000000000000000,x1->1.\
000000000000000000000000000000000000000000000000,x2->1.\
000000000000000000000000000000000000000000000000,x3->1.\
0000000000000000000000000000000000000000000000000,x4->1.\
0000000000000000000000000000000000000000000000000,x5->1.\
0000000000000000000000000000000000000000000000000,abar->0.\
13829898904658144378180892316051003528822699194006,roverw->0}}

Bob Hanlon

---- murat.koyuncu at gmail.com wrote:
> 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
>

```

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