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MathGroup Archive 2007

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Re: Can anybody help me solving such a system of nonlinear equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77654] Re: Can anybody help me solving such a system of nonlinear equations?
  • From: loveinla at gmail.com
  • Date: Thu, 14 Jun 2007 05:34:35 -0400 (EDT)
  • References: <14065758.1181299403027.JavaMail.root@m35>

On Jun 9, 2:42 am, DrMajorBob <drmajor... at bigfoot.com> wrote:
> NSolve (in v6) immediately  (less than 2 seconds) returned one real  
> solution and lots of Complex ones:
>
> NSolve[system, vars]
>
> {{pA -> -12.0619, p1 -> 8.34402, p2 -> 3.35668,
>    disA -> -32.7094}, {pA -> 5.04037+ 0.135893 \[ImaginaryI],
>    p1 -> 2.85233+ 0.141601 \[ImaginaryI],
>    p2 -> 8.05437- 0.100419 \[ImaginaryI],
>    disA -> 0.123062- 1.61597 \[ImaginaryI]}, {pA ->
>     5.04037- 0.135893 \[ImaginaryI],
>    p1 -> 2.85233- 0.141601 \[ImaginaryI],
>    p2 -> 8.05437+ 0.100419 \[ImaginaryI],
>    disA -> 0.123062+ 1.61597 \[ImaginaryI]}, {pA ->
>     3.46024+ 0.739387 \[ImaginaryI],
>    p1 -> 3.05242+ 0.039231 \[ImaginaryI],
>    p2 -> 7.99578+ 0.0164869 \[ImaginaryI],
>    disA -> -0.132054 + 0.565823 \[ImaginaryI]}, {pA ->
>     3.46024- 0.739387 \[ImaginaryI],
>    p1 -> 3.05242- 0.039231 \[ImaginaryI],
>    p2 -> 7.99578- 0.0164869 \[ImaginaryI],
>    disA -> -0.132054 - 0.565823 \[ImaginaryI]}, {pA ->
>     5.12009+ 0.185328 \[ImaginaryI],
>    p1 -> 2.91361+ 0.134372 \[ImaginaryI],
>    p2 -> 4.94667+ 0.0458226 \[ImaginaryI],
>    disA -> 0.173236- 1.66046 \[ImaginaryI]}, {pA ->
>     5.12009- 0.185328 \[ImaginaryI],
>    p1 -> 2.91361- 0.134372 \[ImaginaryI],
>    p2 -> 4.94667- 0.0458226 \[ImaginaryI],
>    disA -> 0.173236+ 1.66046 \[ImaginaryI]}, {pA ->
>     4.11572+ 0.218866 \[ImaginaryI],
>    p1 -> 6.24958- 1.18944 \[ImaginaryI],
>    p2 -> 6.18469+ 1.25056 \[ImaginaryI],
>    disA -> -0.992109 - 1.0035 \[ImaginaryI]}, {pA ->
>     4.11572- 0.218866 \[ImaginaryI],
>    p1 -> 6.24958+ 1.18944 \[ImaginaryI],
>    p2 -> 6.18469- 1.25056 \[ImaginaryI],
>    disA -> -0.992109 + 1.0035 \[ImaginaryI]}, {pA ->
>     4.65713+ 0.303246 \[ImaginaryI],
>    p1 -> 6.1733- 1.1441 \[ImaginaryI],
>    p2 -> 6.18853+ 1.16429 \[ImaginaryI],
>    disA -> -0.14015 + 0.689885 \[ImaginaryI]}, {pA ->
>     4.65713- 0.303246 \[ImaginaryI],
>    p1 -> 6.1733+ 1.1441 \[ImaginaryI],
>    p2 -> 6.18853- 1.16429 \[ImaginaryI],
>    disA -> -0.14015 - 0.689885 \[ImaginaryI]}, {pA ->
>     4.11999+ 0.168207 \[ImaginaryI],
>    p1 -> 6.14997- 1.16879 \[ImaginaryI],
>    p2 -> 6.06909- 1.22008 \[ImaginaryI],
>    disA -> -1.05888 - 1.00133 \[ImaginaryI]}, {pA ->
>     4.11999- 0.168207 \[ImaginaryI],
>    p1 -> 6.14997+ 1.16879 \[ImaginaryI],
>    p2 -> 6.06909+ 1.22008 \[ImaginaryI],
>    disA -> -1.05888 + 1.00133 \[ImaginaryI]}, {pA -> 1.29105,
>    p1 -> 4.62264, p2 -> 3.07625,
>    disA -> -6.77437}, {pA -> 4.61563- 0.275035 \[ImaginaryI],
>    p1 -> 6.09824+ 1.12335 \[ImaginaryI],
>    p2 -> 6.09862+ 1.14324 \[ImaginaryI],
>    disA -> -0.156714 - 0.658444 \[ImaginaryI]}, {pA ->
>     4.61563+ 0.275035 \[ImaginaryI],
>    p1 -> 6.09824- 1.12335 \[ImaginaryI],
>    p2 -> 6.09862- 1.14324 \[ImaginaryI],
>    disA -> -0.156714 + 0.658444 \[ImaginaryI]}, {pA ->
>     3.39423+ 0.689896 \[ImaginaryI],
>    p1 -> 3.11883+ 0.0412614 \[ImaginaryI],
>    p2 -> 4.97625- 0.00736208 \[ImaginaryI],
>    disA -> -0.182116 + 0.514722 \[ImaginaryI]}, {pA ->
>     3.39423- 0.689896 \[ImaginaryI],
>    p1 -> 3.11883- 0.0412614 \[ImaginaryI],
>    p2 -> 4.97625+ 0.00736208 \[ImaginaryI],
>    disA -> -0.182116 - 0.514722 \[ImaginaryI]}, {pA ->
>     4.85856- 1.56365 \[ImaginaryI],
>    p1 -> 6.16703- 1.34382 \[ImaginaryI],
>    p2 -> 6.23016+ 1.1167 \[ImaginaryI],
>    disA -> 0.98401- 1.28569 \[ImaginaryI]}, {pA ->
>     4.85856+ 1.56365 \[ImaginaryI],
>    p1 -> 6.16703+ 1.34382 \[ImaginaryI],
>    p2 -> 6.23016- 1.1167 \[ImaginaryI],
>    disA -> 0.98401+ 1.28569 \[ImaginaryI]}, {pA ->
>     4.69963- 3.76838 \[ImaginaryI],
>    p1 -> 6.35932+ 1.13176 \[ImaginaryI],
>    p2 -> 5.83321+ 1.08874 \[ImaginaryI],
>    disA -> 1.02155- 7.52248 \[ImaginaryI]}, {pA ->
>     4.69963+ 3.76838 \[ImaginaryI],
>    p1 -> 6.35932- 1.13176 \[ImaginaryI],
>    p2 -> 5.83321- 1.08874 \[ImaginaryI],
>    disA -> 1.02155+ 7.52248 \[ImaginaryI]}, {pA ->
>     4.8093- 4.31103 \[ImaginaryI],
>    p1 -> 6.42633+ 1.20204 \[ImaginaryI],
>    p2 -> 6.50206- 1.20925 \[ImaginaryI],
>    disA -> 1.21366- 8.63106 \[ImaginaryI]}, {pA ->
>     4.8093+ 4.31103 \[ImaginaryI],
>    p1 -> 6.42633- 1.20204 \[ImaginaryI],
>    p2 -> 6.50206+ 1.20925 \[ImaginaryI],
>    disA -> 1.21366+ 8.63106 \[ImaginaryI]}, {pA ->
>     4.86385+ 1.55527 \[ImaginaryI],
>    p1 -> 6.10499+ 1.32257 \[ImaginaryI],
>    p2 -> 6.07398+ 1.0823 \[ImaginaryI],
>    disA -> 1.02757+ 1.30923 \[ImaginaryI]}, {pA ->
>     4.86385- 1.55527 \[ImaginaryI],
>    p1 -> 6.10499- 1.32257 \[ImaginaryI],
>    p2 -> 6.07398- 1.0823 \[ImaginaryI],
>    disA -> 1.02757- 1.30923 \[ImaginaryI]}, {pA ->
>     3.38843+ 0.895522 \[ImaginaryI],
>    p1 -> 6.29755- 1.27803 \[ImaginaryI],
>    p2 -> 6.31132+ 1.20406 \[ImaginaryI],
>    disA -> 0.15814+ 1.5184 \[ImaginaryI]}, {pA ->
>     3.38843- 0.895522 \[ImaginaryI],
>    p1 -> 6.29755+ 1.27803 \[ImaginaryI],
>    p2 -> 6.31132- 1.20406 \[ImaginaryI],
>    disA -> 0.15814- 1.5184 \[ImaginaryI]}, {pA -> 13.8105,
>    p1 -> 2.4038, p2 -> 8.79103,
>    disA -> 18.7794}, {pA -> 4.1733- 0.324981 \[ImaginaryI],
>    p1 -> 2.29099+ 0.0766739 \[ImaginaryI],
>    p2 -> 2.3076+ 0.0406625 \[ImaginaryI],
>    disA -> -0.710154 - 1.18873 \[ImaginaryI]}, {pA ->
>     4.1733+ 0.324981 \[ImaginaryI],
>    p1 -> 2.29099- 0.0766739 \[ImaginaryI],
>    p2 -> 2.3076- 0.0406625 \[ImaginaryI],
>    disA -> -0.710154 + 1.18873 \[ImaginaryI]}, {pA ->
>     3.46353- 0.931219 \[ImaginaryI],
>    p1 -> 6.22396+ 1.23016 \[ImaginaryI],
>    p2 -> 5.97284+ 1.13346 \[ImaginaryI],
>    disA -> 0.201138- 1.55057 \[ImaginaryI]}, {pA ->
>     3.46353+ 0.931219 \[ImaginaryI],
>    p1 -> 6.22396- 1.23016 \[ImaginaryI],
>    p2 -> 5.97284- 1.13346 \[ImaginaryI],
>    disA -> 0.201138+ 1.55057 \[ImaginaryI]}, {pA ->
>     4.70041- 0.960206 \[ImaginaryI],
>    p1 -> 2.32094+ 0.0471748 \[ImaginaryI],
>    p2 -> 2.2751+ 0.0383211 \[ImaginaryI],
>    disA -> 1.03635- 1.34182 \[ImaginaryI]}, {pA ->
>     4.70041+ 0.960206 \[ImaginaryI],
>    p1 -> 2.32094- 0.0471748 \[ImaginaryI],
>    p2 -> 2.2751- 0.0383211 \[ImaginaryI],
>    disA -> 1.03635+ 1.34182 \[ImaginaryI]}, {pA ->
>     4.36828- 2.33519 \[ImaginaryI],
>    p1 -> 4.86511- 0.121694 \[ImaginaryI],
>    p2 -> 3.02683+ 0.00790086 \[ImaginaryI],
>    disA -> -0.520092 - 2.76693 \[ImaginaryI]}, {pA ->
>     4.36828+ 2.33519 \[ImaginaryI],
>    p1 -> 4.86511+ 0.121694 \[ImaginaryI],
>    p2 -> 3.02683- 0.00790086 \[ImaginaryI],
>    disA -> -0.520092 + 2.76693 \[ImaginaryI]}, {pA -> 4.55414,
>    p1 -> 2.30068, p2 -> 2.26998, disA -> 1.10028}, {pA -> 4.12886,
>    p1 -> 4.9679, p2 -> 3.10847,
>    disA -> -0.118869}, {pA -> 5.34263+ 1.29037 \[ImaginaryI],
>    p1 -> 7.96453+ 0.077481 \[ImaginaryI],
>    p2 -> 3.02181+ 0.00290677 \[ImaginaryI],
>    disA -> 0.325702+ 1.01253 \[ImaginaryI]}, {pA ->
>     5.34263- 1.29037 \[ImaginaryI],
>    p1 -> 7.96453- 0.077481 \[ImaginaryI],
>    p2 -> 3.02181- 0.00290677 \[ImaginaryI],
>    disA -> 0.325702- 1.01253 \[ImaginaryI]}, {pA -> 4.01023,
>    p1 -> 4.96928, p2 -> 3.03291, disA -> 1.7214}, {pA -> 17.2655,
>    p1 -> 2.43961, p2 -> 4.61844,
>    disA -> 25.6739}, {pA -> 3.09831+ 0.527086 \[ImaginaryI],
>    p1 -> 8.13816+ 0.0758926 \[ImaginaryI],
>    p2 -> 3.05628+ 0.0238497 \[ImaginaryI],
>    disA -> -0.330776 - 1.208 \[ImaginaryI]}, {pA ->
>     3.09831- 0.527086 \[ImaginaryI],
>    p1 -> 8.13816- 0.0758926 \[ImaginaryI],
>    p2 -> 3.05628- 0.0238497 \[ImaginaryI],
>    disA -> -0.330776 + 1.208 \[ImaginaryI]}}
>
> Bobby
>
>
>
>
>
> On Fri, 08 Jun 2007 04:38:26 -0500, <lovei... at gmail.com> wrote:
> > Hi, guys,
>
> > I have tried NSolve, Solve, Reduce, to solve the system below,
> > however, the mathematica didn't return an answer. Can anybody know how
> > to solve it using Mathematica?
>
> > The inputs are as follows:
>
> > a = 24;
> > b = 5;
> > c = 25;
> > d = 4;
> > cA = 3;
> > cB = 2;
> > t = 5;
> > alpha = 0.2;
> > Solve[{(a - b*pA - b*(pA - cA))*(0.5 - ((d/2)(
> > p1^2 - p2^2) -
> >     c(p1 - p2))/(2t) - ((b/2)((pA - disA)^2 - pA^2) +
> >               a*disA)/(2t)) - ((p1 - cB)(
> >           c - d*p1) + (
> >               pA - disA - cA)(a - b*(pA - disA)) - (pA -
> >                     cA)(a - b*(pA)))*(-(a - b*pA)/(2t)) ==
> >               0, -(a - b*(pA - disA) - b(pA - disA - cA))*(0.5 + ((d/2)
> > (
> >                     p1^2 - p2^2) - c(p1 - p2))/(2t) + ((
> >         b/2)((pA - disA)^2 - pA^2) + a*disA)/(2t)) - ((
> >               p1 - cB)(c - d*p1) + (pA - disA - cA)(a -
> >                     b*(pA - disA)) - (pA - cA)(a - b*(
> >               pA)))*(-(a - b*(pA - disA))/(2t)) == 0, ((p1 -
> >            cB)(c - d*p1) + alpha*(pA - disA - cA)(a - b*(
> >     pA - disA)) - alpha*(pA - cA)(a - b*(pA)))*(-(
> >                 c - d*p1)/(2t)) + (c - d*p1 - d(p1 - cB))(0.5 + ((d/
> >               2)(p1^2 - p2^2) - c(p1 - p2))/(2t) + alpha*((
> >                     b/2)((pA - disA)^2 - pA^2) + a*disA)/(
> >               2t)) == 0, (c - d*p2 - d*(p2 - cB))(0.5 - ((d/
> >                           2)(p1^2 - p2^2) - c(p1 - p2))/(2t) -
> > alpha*((b/
> >         2)((pA - disA)^2 - pA^2) + a*disA)/(2t)) + (
> >               p2 - cB)(c - d*p2)(-(c - d*p2)/(2t)) == 0}, {pA, p1,p2,
> > disA}]
>
> > Thank you in advance.
>
> --
> DrMajor... at bigfoot.com- Hide quoted text -
>
> - Show quoted text -

Thanks a lot! I finally got the solution


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