system of equations
- To: mathgroup at smc.vnet.net
- Subject: [mg73340] system of equations
- From: Lena Calahorrano <lena.calahorrano at rwth-aachen.de>
- Date: Tue, 13 Feb 2007 06:55:24 -0500 (EST)
Maybe someone can help me solving a system of equations:
I have two equations each of which depends on the the two variables =E2=80
=9Ckheute=E2=80=9D and =E2=80=9CMheute=E2=80=9D and I am interested in the
value of these two variables.
The equations look like this, where all parameters are known:
kheute=C5=A0l*(1/(1+n)*((1-a)*A*Part[f[t],1]^a*(b^2/f+b/f)-(1-a)*A*kheute^a
/(1+a*A*kheute^(a-1)-d))+1/(1+n)^2*b^2/f*((1-a)*A*Part[f[t],1]^a+(1+a*A*Part[f[t],1]^(a-1)-d)*(1-a)*A*Part[f[t-1],1]))/((2+n)/(1+n)+Mheute/bev)
kheute====l*(1/(1+An)*((1-a)*A*Part[Af[t],1]^a*(b^2/f+b/f)-(1-a)*A*kheute^a/(1+a*A*kheute^(a-1)-d))+1/(1+An)^2*b^2/f*((1-a)*A*Part[Af[t],1]^a+(1+a*A*Part[Af[t],1]^(a-1)-d)*(1-a)*A*Part[Af[t-1],1]))/((2+An)/(1+An)-Mheute/bevA)
I can express =E2=80=9Ckheute=E2=80=9D as a function of =E2=80=9CMheute=E2=80=9D, I can plot the two functions and see where they intersect:
solInland==Solve[Simplify[kheute=C5=A0l*(1/(1+n)*((1-a)*A*Part[f[t],1]^a*(b^2/f+b/f)-(1-a)*A*kheute^a/(1+a*A*kheute^(a-1)-d))+1/(1+n)^2*b^2/f*((1-a)*A*Part[f[t],1]^a+(1+a*A*Part[f[t],1]^(a-1)-d)*(1-a)*A*Part[f[t-1],1]))/((2+n)/(1+n)+Mheute/bev)],Mheute]
mInland==Part[Mheute/.solInland,1]
f[kheute_]:==mInland
grafikInland==Plot[f[kheute],{kheute,0.04,0.14},PlotStyle=C2=AE{RGBColor[1,0, 0.501961]}];
solAusland==Solve[Simplify[kheute====l*(1/(1+An)*((1-a)*A*Part[Af[t],1]^a*(b^2/f+b/f)-(1-a)*A*kheute^a/(1+a*A*kheute^(a-1)-d))+1/(1+An)^2*b^2/f*((1-a)*A*Part[Af[t],1]^a+(1+a*A*Part[Af[t],1]^(a-1)-d)*(1-a)*A*Part[Af[t-1],1]))/((2+An)/(1+An)-Mheute/bevA)],Mheute]
mAusland==Part[Mheute/.solAusland,1]
g[kheute_]:==mAusland
grafikAusland==Plot[g[kheute],{kheute,0.04,0.14}];
vergl==Show[grafikInland,grafikAusland];
But when I try to solve for =E2=80=9Ckheute=E2=80=9D, Mathematica runs forever. This is a problem because I eventually want to compute about 50 more steps.
Solve[Simplify[mInland=C5=A0mAusland],kheute]
Is there a better way to do this kind of computation?
Best regards,
Lena Calahorrano
Lena Calahorrano
Lehr- und Forschungsgebiet
Internationale Wirtschaftsbeziehungen
RWTH Aachen
Templergraben 64
52056 Aachen
0241-80-93934
lena.calahorrano at rwth-aachen.de
http://www.iw.rwth-aachen.de