Re: Cannot NSolve a system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg88938] Re: Cannot NSolve a system of equations
• From: dh <dh at metrohm.ch>
• Date: Wed, 21 May 2008 14:54:20 -0400 (EDT)
• References: <g0uahi\$4tk\$1@smc.vnet.net>

```
Hi Murat,

try to check your equations not with Equal, but subtract the left from

the right side. E.g. by:

eqns1 /. Equal -> Subtract /. sol

As you are working with machine numbers, you can not expect an 100%

accurate solution. In your case, you will see that the equations are

o.k. with an error better than 10^-8.

This is not overwhelming, but may be good enough for your purpose. If

not, one can consider: Rationalizing, Condition number of equations,

Arbitrary precision calculation etc.

hope this helps, Daniel

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

>

--

Daniel Huber

Metrohm Ltd.

Oberdorfstr. 68

CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>

```

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