Solve and parametric nonlinear equations
- To: mathgroup at smc.vnet.net
- Subject: [mg93771] Solve and parametric nonlinear equations
- From: "alessandro tavoni" <atavoni at Princeton.EDU>
- Date: Tue, 25 Nov 2008 07:18:28 -0500 (EST)
Hello, I am newbie to Mathematica 6, and I am having some difficulties with
Solve.
I have a two algebraic equations in two variables and two parameters and I
need to numerically solve the system over an interval of values for the
parameters.
When using Solve, I get the message: Solve::tdep: The equations appear to
involve the variables to be solved for in an essentially non-algebraic way.
I tried several alternative approaches, but no one worked. Findroot works
fine, but I need the symbolic solution since I am interested in the values
of the solutions when the parameters alfa and beta change. To simplify
matters, I assign a numerical value to lambda, but that's not enough to make
it analytically solvable apparently. Here's the code:
\[Lambda] = .43
\!\(\*OverscriptBox["U1",
RowBox[{"\[IndentingNewLine]", "DifR"}]]\) = 14 - 6 \[Beta]
\!\(\*OverscriptBox["U1", "UifR"]\) = 4 - 18 \[Alpha]
\!\(\*OverscriptBox["U1", "UifL"]\) = 10 - 2 \[Alpha]
\!\(\*OverscriptBox["U1", "DifL"]\) = 9
\!\(\*OverscriptBox["U2", "LifD"]\) = 9
\!\(\*OverscriptBox["U2", "RifD"]\) = 8 - 6 \[Alpha]
\!\(\*OverscriptBox["U2", "RifU"]\) = 22 - 18 \[Beta]
\!\(\*OverscriptBox["U2", "LifU"]\) = 12 - 2 \[Beta]
eq1 = Pu == \[ExponentialE]^(\[Lambda] (
\!\(\*OverscriptBox["U1", "UifL"]\) Ql +
\!\(\*OverscriptBox["U1",
"UifR"]\) (1 - Ql)))/(\[ExponentialE]^(\[Lambda] (
\!\(\*OverscriptBox["U1", "UifL"]\) Ql +
\!\(\*OverscriptBox["U1",
"UifR"]\) (1 - Ql))) + \[ExponentialE]^(\[Lambda] (
\!\(\*OverscriptBox["U1", "DifL"]\) Ql +
\!\(\*OverscriptBox["U1", "DifR"]\) (1 - Ql))))
eq2 = Ql == \[ExponentialE]^(\[Lambda] (
\!\(\*OverscriptBox["U2", "LifU"]\) Pu +
\!\(\*OverscriptBox["U2",
"LifD"]\) (1 - Pu)))/(\[ExponentialE]^(\[Lambda] (
\!\(\*OverscriptBox["U2", "LifU"]\) Pu +
\!\(\*OverscriptBox["U2",
"LifD"]\) (1 - Pu))) + \[ExponentialE]^(\[Lambda] (
\!\(\*OverscriptBox["U2", "RifU"]\) Pu +
\!\(\*OverscriptBox["U2", "RifD"]\) (1 - Pu))))
Solve[{eq1, eq2}, {Pu, Ql}]
Any suggestions would be much appreciated,
Alessandro
--
Alessandro Tavoni
Ph.D. candidate
Advanced School of Economics, University of Venice "C=E0 Foscari"
<http://venus.unive.it/alessandro.tavoni>
http://venus.unive.it/alessandro.tavoni
LevinLab member <http://www.eeb.princeton.edu/~slevin/Labdirectory.html>
at
Princeton University