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Student Support Forum: 'Numerically solve coupled equations' topicStudent Support Forum > General > "Numerically solve coupled equations"

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Daniel
10/17/12 4:23pm

I have three coupled implicit equations which I would like to solve numerically. The implicit equations may yield complex results, in general, and I need to discard the negative root and calculate only with the positive one. Here is what I have so far:


\[CapitalDelta] := 4
Ux := 1
Uy := 1 + \[CapitalDelta]/3
Uz := 2 \[CapitalDelta]
e1 := 0.5
e2 := 12
f1 := 0.5
f2 := 1 - f1


Da := 1/(4*\[Pi])*
NIntegrate[(Sin[\[Theta]]^3*Cos[\[Phi]]^2)/(Ux^2*\[Rho]), {\[Phi],
0, 2 \[Pi]}, {\[Theta], 0, \[Pi]}]
Db := 1/(4*\[Pi])*
NIntegrate[(Sin[\[Theta]]^3*Sin[\[Phi]]^2)/(Uy^2*\[Rho]), {\[Phi],
0, 2 \[Pi]}, {\[Theta], 0, \[Pi]}]
Dc := 1/(4*\[Pi])*
NIntegrate[(Sin[\[Theta]]*Cos[\[Phi]]^2)/(Uz^2*\[Rho]), {\[Phi], 0,
2 \[Pi]}, {\[Theta], 0, \[Pi]}]
\[Rho] := ((Sin[\[Theta]]^2*Cos[\[Phi]]^2*eff1)/
Ux^2 + (Sin[\[Theta]]^2*Sin[\[Phi]]^2*eff2)/
Uy^2 + (Cos[\[Phi]]^2*eff3)/Uz^2)


sols1 := eff1 /.
NSolve[f1 ((e1 - eff1)/(1 + Da*(e1 - eff1))) +
f2 ((e2 - eff1)/(1 + Da*(e2 - eff1))) == 0 && 20 > Re[eff1] > 0,
eff1]
sols2 := eff2 /.
NSolve[f1 ((e1 - eff2)/(1 + Db*(e1 - eff2))) +
f2 ((e2 - eff2)/(1 + Db*(e2 - eff2))) == 0 && 20 > Re[eff2] > 0,
eff2]
sols3 := eff3 /.
NSolve[f1 ((e1 - eff3)/(1 + Dc*(e1 - eff3))) +
f2 ((e2 - eff3)/(1 + Dc*(e2 - eff3))) == 0 && 20 > Re[eff3] > 0,
eff3]

sol = Solve[{sols1, sols2, sols3}, {eff1, eff2, eff3}]

The last line is obviously what I would like to calculate, but it does not work since "the integrand in the 'D's has evaluated to non-numerical values"

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Subject (listing for 'Numerically solve coupled equations')
Author Date Posted
Numerically solve coupled equations Daniel 10/17/12 4:23pm
Re: Numerically solve coupled equations Bill Simpson 10/18/12 00:48am
Re: Numerically solve coupled equations Daniel 10/23/12 01:29am
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