Re: Solve problems

• To: mathgroup at smc.vnet.net
• Subject: [mg64251] Re: [mg64233] Solve problems
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 8 Feb 2006 03:53:39 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```eqns1=Rationalize[{
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=N[Solve[eqns1,
{c1,c2,c3,c4,c5,c6,c7,c8}],20];

eqns1/.sol

{{True, True, True, True, True, True, True, True},
{True, True, True, True, True, True, True, True},
{True, True, True, True, True, True, True, True},
{True, True, True, True, True, True, True, True},
{True, True, True, True, True, True, True, True}}

Bob Hanlon

>
> From: Joerg Schaber <schaber at molgen.mpg.de>
To: mathgroup at smc.vnet.net
> Subject: [mg64251] [mg64233] Solve problems
>
> 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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