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MathGroup Archive 2007

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Re: My problem when solving a system of equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg78071] Re: My problem when solving a system of equations
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Fri, 22 Jun 2007 06:40:52 -0400 (EDT)
  • References: <f5dkv7$13j$1@smc.vnet.net>

Hi.

Quit the session.
This is what I got.

In[1]:=
a = 24;
b = 5;
c = 25;
d = 4;
cA = 3;
cB = 2;
t = 5;
alpha = 0;
bta = 0.6;
NB = NSolve[{-d(p - cB) + c - d*p == (p - cB)(c - d*p)^2/t}, {p}];
SNB = DeleteCases[NB, {p -> _Complex}]
B = NSolve[{(alpha + (1 - alpha - bta)*(0.5 - ((d/
2)*(p1^2 - p2^2) - c*(p1 - p2))/(2t) - ((b/2)*((
pA - disA)^2 - pA^2) + a*disA)/(2t)))*(a - b*pA - b*(pA -
cA)) - (1 - alpha - bta)*((p1 - cB)*(c - d*
p1) + (pA - disA - cA)*(a - b*(pA -
disA)) - (pA - cA)*(a - b*pA))*(-(
a - b*pA)/(
2t)) == 0, (1 - alpha - bta)*((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, (1 - alpha)*((c - d*p1 - d*(p1 -
cB))*(0.5 + ((d/2)*(p1^2 - p2^2) - c*(p1 -
p2))/(2t)) + (p1 - cB)*(c - d*p1)*(-
c + d*p1)/(2t)) + (1 -
alpha - bta)*(((pA - disA - cA)*(a -
b*(pA - disA)) - (pA - cA)*(a - b*
pA))*(-c + d*p1)/(2t) + (c - d*p1 - d(
p1 - cB))*((
b/2)((pA - disA)^2 - pA^2) + a*disA)/(2t)) ==
0, (1 - alpha)*((c - d*p2 - d(p2 - cB))*(
0.5 - ((d/
2)*(p1^2 - p2^2) - c*(p1 - p2))/(2t)) + (
p2 - cB)*(c - d*p2)*(-c + d*p2)/(
2t)) - (1 - alpha - bta)*(c - d*p2 - d(p2 -
cB))*((
b/2)*((pA - disA)^2 - pA^2) + a*disA)/(
2t) == 0}, {pA, p1, p2, disA}];
BR = DeleteCases[B, {pA -> _Complex, p1 -> _Complex,
p2 -> _Complex, disA -> _Complex}];
SB = Select[BR, And @@ (({pA > 0, p1 > 0, p2 >
0, disA > 0, pA - disA > 0} /. #)) &]


Out[11]=
{{p\[Rule]2.29251}}

>From In[1]:=
\!\(\*
  RowBox[{\(General::"ovfl"\), \(\(:\)\(\ \)\), "\<\"Overflow occurred
in
      computation. \\!\\(\\*
      ButtonBox[\\\"More...\\\", ButtonStyle->\\\"RefGuideLinkText\\\",
\
ButtonFrame->None, ButtonData:>\\\"General::ovfl\\\"]\\)\"\>"}]\)

>From In[1]:=
\!\(\*
  RowBox[{\(General::"ovfl"\), \(\(:\)\(\ \)\), "\<\"Overflow occurred
in
      computation. \\!\\(\\*
      ButtonBox[\\\"More...\\\", ButtonStyle->\\\"RefGuideLinkText\\\",
\
ButtonFrame->None, ButtonData:>\\\"General::ovfl\\\"]\\)\"\>"}]\)

>From In[1]:=
\!\(\*
  RowBox[{\(General::"ovfl"\), \(\(:\)\(\ \)\), "\<\"Overflow occurred
in
      computation. \\!\\(\\*
      ButtonBox[\\\"More...\\\", ButtonStyle->\\\"RefGuideLinkText\\\",
\
ButtonFrame->None, ButtonData:>\\\"General::ovfl\\\"]\\)\"\>"}]\)

>From In[1]:=
\!\(\*
  RowBox[{\(General::"stop"\), \(\(:\)\(\ \)\), "\<\"Further output
    of \\!\\(General :: \\\"ovfl\\\"\\) will be suppressed during this
\
calculation. \\!\\(\\*ButtonBox[\\\"More...\\\", \
ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \
ButtonData:>\\\"General::stop\\\"]\\)\"\>"}]\)

Out[14]=
{{pA\[Rule]3.\
973243201739556412519288128044045997023945804915557029065972720546420058294383\
598890842765930734752225321438217919715672292159,p1\[Rule]4.\
958302020595319842684443749027684798737496883013818475220698244283505299552283\
746464263057828871991290065319494660363196793637,p2\[Rule]2.\
949204312095856784866178070015229092944379297947239512443226175303784609762982\
212035816978006166136210705386558781550333832228,disA\[Rule]1.\
731734509545513083657459575251578321354802750093079646091000411298081255083276\
2752868835871074875089387169154659532655501459707},{pA\[Rule]4.\
445374167300070939184859858213378678822259958732577495895907507151618691880549\
660415122202305507338705522502612851605862635436,p1\[Rule]2.\
319154466638120757503327374403506997877094995315975812555535812309131709076747\
313776308520736763603708360710094963211884291417,p2\[Rule]2.\
253920247454767926310848830750026635205895182591143116593491779431290407927731\
601498154267807767823951092934390534865277197642,disA\[Rule]0.\
996606632207799253314486632859463384535676075471633096023971809376766993819562\
5934892093572991329922317150799668794322107434808}}

Dimitris


lovei... at gmail.com       :
> Hi, guys,
>
> I was trying to solve a system of nonlinear equations. However,
> whenever I run it, Mathematica always returns:
> " ReplaceAll::reps: {-0.04\(-24 + 5\pA)\((25 - 4\p1)\(-2 + p1) - (24 -
> \
> 5\pA)\(-3 + pA) + (-3 - disA + pA)\(24 - 5\(-disA + pA))) + 0.4\(\
> \[LeftSkeleton]1\[RightSkeleton])\(\[LeftSkeleton]1\[RightSkeleton])
> == 0, \
> \[LeftSkeleton]3\[RightSkeleton]} is neither a list of replacement
> rules nor \
> a valid dispatch table, and so cannot be used for replacing. "
>
> I don't know what this means and how to deal with it.
>
> Below is my code for your reference:
>
> a = 24;
> b = 5;
> c = 25;
> d = 4;
> cA = 3;
> cB = 2;
> t = 5;
> alpha = 0;
> bta = 0.6;
> NB = NSolve[{-d(p - cB) + c - d*p == (p - cB)(c - d*p)^2/t}, {p}];
> SNB = DeleteCases[NB, {p -> _Complex}]
> B = NSolve[{(alpha + (1 - alpha - bta)*(0.5 - ((d/
>           2)*(p1^2 - p2^2) - c*(p1 - p2))/(2t) - ((b/2)*((
>       pA - disA)^2 - pA^2) + a*disA)/(2t)))*(a - b*pA - b*(pA -
>     cA)) - (1 - alpha - bta)*((p1 - cB)*(c - d*
>     p1) + (pA - disA - cA)*(a - b*(pA -
>                    disA)) - (pA - cA)*(a - b*pA))*(-(
>                     a - b*pA)/(
>                         2t)) == 0, (1 - alpha - bta)*((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, (1 - alpha)*((c - d*p1 - d*(p1 -
>                   cB))*(0.5 + ((d/2)*(p1^2 - p2^2) - c*(p1 -
>                         p2))/(2t)) + (p1 - cB)*(c - d*p1)*(-
>                   c + d*p1)/(2t)) + (1 -
>                      alpha - bta)*(((pA - disA - cA)*(a -
>
>                   b*(pA - disA)) - (pA - cA)*(a - b*
>         pA))*(-c + d*p1)/(2t) + (c - d*p1 - d(
>             p1 - cB))*((
>                       b/2)((pA - disA)^2 - pA^2) + a*disA)/(2t)) ==
>                           0, (1 - alpha)*((c - d*p2 - d(p2 - cB))*(
>         0.5 - ((d/
>                   2)*(p1^2 - p2^2) - c*(p1 - p2))/(2t)) + (
>                         p2 - cB)*(c - d*p2)*(-c + d*p2)/(
>                         2t)) - (1 - alpha - bta)*(c - d*p2 - d(p2 -
> cB))*((
>                               b/2)*((pA - disA)^2 - pA^2) + a*disA)/(
>                   2t) == 0}, {pA, p1, p2, disA}];
> BR = DeleteCases[B, {pA -> _Complex, p1 -> _Complex,
>              p2 -> _Complex, disA -> _Complex}];
> SB = Select[BR, And @@ (({pA > 0, p1 > 0, p2 >
>                0, disA > 0, pA - disA > 0} /. #)) &]



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