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MathGroup Archive 2006

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Re: Solve problems

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64250] Re: Solve problems
  • From: dh <dh at metrohm.ch>
  • Date: Wed, 8 Feb 2006 03:53:38 -0500 (EST)
  • References: <ds9nfl$91$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Joerg,
Calculations with approximate (Real) numbers do not give accurate 
results. Therefore, calculate the "error" of your solution and you will 
see that the errors are about 10^-15 and smaller. That is fine 
considering that you use approximate arithmetic.

Daniel

Joerg Schaber wrote:
> Hi,
> 
> I have a system of polynomial equations where Solve cannot find the
> right solutions. Any hints? By the way, actually I just want to find the
> steady states of a differential equation system. If there is another
> clever way, please let me know.
> There are also coonstraints that all variable must be >=0, but including 
> those constraints and using Reduce also does not yield a valid solution. 
> There exisits a valid solution. I checked this solving the differential 
> equation system with NDSolve and let it run into the steady state. But 
> this is not very elegant and principally the steady states can be 
> calculated directly.
> 
> eqns1={0 == 0. c1 + 0.001 c3 - 721.9 c1 c4 + 0.001 c2 c8,
> 0 == 0.001 c3 - 721.9 c1 c4 + 0.001 c5 - 346.09 c4 c6,
> 0 == 0.001 c5 - 346.09 c4 c6 - 989.77 c6 c7 + 0.001 c8,
> 0 == -989.77 c6 c7 + 0.001 c8, c1 + c2 + c3 == 5.7,
> c3 + c4 + c5 == 19.3,
> c5 + c6 + c8 == 4.,
> c7 + c8 == 1.};
> 
> sol = Solve[eqns1, {c1, c2, c3, c4, c5, c6, c7, c8}, VerifySolutions ->
> True];
> 
> \!\({{c2 -> 0.`, c3 ->
>          5.69999921807596`, c5 -> 3.502051416006559`, c1 -> \
> 7.819240400365867`*^-7, c7 -> 0.5020524180816763`, c8 -> 
> 0.4979475819183236`, \
> c6 -> 1.0020751177226038`*^-6, c4 -> 10.097949365917481`}, {c2 -> 0.`, 
> c3 -> \
> 5.699999640315395`,
>        c5 -> \(-8.352092810365317`\), c1 -> 3.5968460447115093`*^-7,
>           c7 -> \(-11.352093909700997`\), c8 -> 12.352093909700997`, c6 -> \
> \(-1.0993356796497231`*^-6\), c4 -> 21.95209317004992`}, {c2 -> 0.`,
>        c3 -> 8.687577015258206`, c5 -> 10.612427012862872`,
>        c1 -> \(-2.987577015258207`\), c7 -> \(-1.3272190975834564`*^-7\),
>          c8 -> 1.0000001327219097`, c6 -> \(-7.612427145584781`\),
>         c4 -> \(-4.028121078693263`*^-6\)}, {c2 -> 0.`, c3 -> \
> 19.300001049304143`,
>          c5 -> 9.165049916617935`*^-7, c1 -> \(-13.600001049304144`\), 
> c7 -> \
> \(-3.0000004306092727`\), c8 -> 4.000000430609273`,
>          c6 -> \(-1.3471142644128086`*^-6\), c4 -> \
> \(-1.965809135229149`*^-6\)}, {c2 -> 0.`,
>          c3 -> 24.324407481766347`, c5 -> \(-5.024405672582244`\), c1 -> \
> \(-18.624407481766347`\), c7 -> 1.259078407457304`*^-7, c8 -> \
> 0.9999998740921593`, c6 -> 8.024405798490085`,
>         c4 -> \(-1.8091841042296682`*^-6\)}}\)
> 
> 
> Einsetzen ergibt:
> 
> eqns1 /. sol
> 
> {{True, False, False, False, True, True, True, True}, {True, True,
>      False, False, True, True, True, True}, {True, False, False, True,
>      True, True, True, True}, {True, False, True, True, True, True,
>      True, True}, {False, False, False, True, True, True, True, True}}
> 
> 
> best wishes,
> 
> joerg
> 


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