I have the following system of 27 equations:
{pb λ10 + λ12 + 0.99 (-0.995 (0.04 + 0.96 pb) λ10 -
pb (0.0025 + 0.972 Rb - 0.972 Rd) λ3) + pb λ7 - 1/2 λ12 Erfc[
2.11216 (0.021975 + 2 (0.150823 + Log[B]))] == 0, 1/c - 3.409 L^0.5 λ1 - λ13 - λ2/c^2 - ( 0.99 (-Rd + Rk) λ5 (1 +
0.972 (-1 + (0.3863 νz)/(0.3863 - νk))))/ c + ((1 + Rd) λ2 +
c (-Rd + Rk) λ5 (1 +
0.972 (-1 + (0.3863 νz)/(0.3863 - νk))) +
c λ6 (1 +
0.972 (-1 + (0.3863 νz)/(0.3863 - νk))) (1 +
Rd - τz))/c^2 - ( 0.99 λ6 (1 +
0.972 (-1 + (0.3863 νz)/(0.3863 - νk))) (1 +
Rd - τz))/c == 0, -1.728 inv pk λ8 == 0, (1/( K^2 L^0.33))(-K^2 L^0.33 (0.058906 λ13 +
pk (0.002475 λ3 - 0.96228 Rd λ3 +
0.96228 Rk λ3 - λ7)) +
0.218889 K^0.33 L λ9 +
0.3267 K^1.33 (-0.67 λ1 (-1 + τh) +
L (λ13 + 0.67 λ10 τh))) == 0, (1/( K L^1.33))(K (-3.409 L^0.83 (L + 0.5 c λ1) +
1. K^0.33 L (λ13 + λ10 τh)) +
0.1089 K^0.33 (L λ9 +
K (λ1 - λ1 τh + L λ10 τh)) -
0.33 K^0.33 (L λ9 +
K (λ1 + L λ13 - λ1 τh +
2 L λ10 τh))) == 0, ( 0.995 (0.0396 - 0.0096 pb) λ11 + B pb^2 (0.0448 λ10 - 0.002475 λ3 -
0.96228 Rb λ3 + 0.96228 Rd λ3 + λ7))/ pb^2 == 0, K (-0.002475 λ3 + 0.96228 Rd λ3 -
0.96228 Rk λ3 + λ7) + λ8 + (0.0394 +
0.99 Rk) λ9 == 0, λ11 - 0.972 B pb λ3 == 0, -(λ2/c) + 0.972 B pb λ3 + 0.972 K pk λ3 - 0.972 Z λ3 + 0.028 λ5 - 0.028 λ6 + 0.972 λ5 νz - 0.972 λ6 νz + (0.972 λ5 νk νz)/( 0.3863 - νk) - (0.972 λ6 νk νz)/( 0.3863 - νk) == 0, -0.972 K pk λ3 + pk λ9 + λ5 (-0.028 - (0.375484 νz)/(
0.3863 - νk)) == 0, λ3 - (λ7 νz)/(0.3863 - νk) + 0.99 (-0.972 (1 + Rd) λ3 + (λ10 + λ3) τz) == 0, (-3.409 c L^0.83 - 0.67 K^0.33 (-1 + τh))/L^0.33 == 0, -0.2 K^0.33 L^0.67 - 0.995 B (0.04 + 0.96 pb) + B pb + 0.67 K^0.33 L^0.67 τh + Z τz == 0, -((0.995 (0.04 + 0.96 pb))/pb) + Rb == 0, -0.86 + B + 0.431301 Erfc[4.22432 (0.133791 + Log[B])] - 1/2 B Erfc[4.22432 (0.16181 + Log[B])] == 0, -c - 0.0494 K + 0.8 K^0.33 L^0.67 == 0, (1 - 0.99 (1 + Rd))/c == 0, -B pb (0.0025 + 0.972 Rb - 0.972 Rd) + K pk (-0.0025 + 0.972 Rd - 0.972 Rk) + Z (1 - 0.972 (1 + Rd) + τz) == 0, νk - 0.99 (-Rd + Rk) (1 +
0.972 (-1 + (0.3863 νz)/(0.3863 - νk))) == 0, νz - 0.99 (1 + 0.972 (-1 + (0.3863 νz)/(0.3863 - νk))) (1 + Rd - τz) == 0, B pb + K pk - (Z νz)/(0.3863 - νk) == 0, -1 + pk == 0, -((0.33 L^0.67)/K^0.67) + pk (0.0494 + Rk) == 0, ( 0.149228 λ5 + λ5 νk^2 - Z λ7 νz - 0.3863 (λ5 (2 νk + 0.972 (-Rd + Rk) νz) + 0.972 λ6 νz (1 +
Rd - τz)))/(0.3863 - νk)^2 == 0, (-0.375484 Rk λ5 + 0.375484 Rd (λ5 - λ6) + 0.0108164 λ6 - Z λ7 - λ6 νk + 0.375484 λ6 τz)/(0.3863 - νk) == 0, -((0.67 K^0.33 (λ1 - L λ10))/L^0.33) == 0, Z (λ10 + λ3) + λ6 (1 + 0.972 (-1 + (0.3863 νz)/(0.3863 - νk))) == 0}
There are 27 Real variables : B, c, inv, K, L, pb, pk, Rb, Rd, Rk, Z, λ1, λ10, λ11, λ12, λ13, λ2, λ3, λ5, λ6, λ7, λ8, λ9, νk, νz, τh, τz
.
Can anyone please give me some hint on how to find a solution of this system in Mathematica? I have tried the command NSolve
and FindRoot
but don't manage to calculate it. Note that Greek letter variables can be positive or negative, while the others can only be positive.
K
is a system symbol and shouldn't be used as a variable name. $\endgroup$ – Szabolcs Dec 1 '16 at 11:43NSolve
will work unless you can bound the variables (because ofErfc
and perhaps the inexact0.33
powers).FindRoot
might find one root at a time, if it has a good starting point for the variables. $\endgroup$ – Michael E2 Dec 1 '16 at 11:54FindMinimum
work at it. However I have little hope you will solve that unless you can make a very good initial guess at all 27 unknowns. $\endgroup$ – george2079 Dec 1 '16 at 16:09