I have this nonlinear system to solve,

phi1=((A1)/(1-K(1,1)*A1)^2)*(1+((V(1,1)*KAB*B1)/(V(2,1)*(1-K(2,1)*B1))));

phi2=((B1)/(1-K(2,1)*B1)^2)*(1+((KAB*A1)/(1-K(1,1)*A1)));

With some help, I started to solve with fsolve, but I need A1 and B1 between 0 and 1.

I tried to put this in lsqnonlin, but it is not working.

Could somebody help me to solve this? What I have to do to have values between 0 and 1?

Is this the better way to solve this system?

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function [phi] = Test

V=[18.068;55.918];

K=[1005;213.2];

KAB=50;

phi1=[0.121;0.214;0.341;0.423;0.512;0.611;0.731;0.834;0. 925];

%phi2=1-phi1;

n=numel(phi1);

%f1=-phi1+((A1)/(1-K(1,1)*A1)^2)*(1+((V(1,1)*KAB*B1)/(V(2,1)*(1-K(2,1)*B1))));

%f2=-phi2+((B1)/(1-K(2,1)*B1)^2)*(1+((KAB*A1)/(1-K(1,1)*A1)));

for i = 1:n;

phi1_scal = phi1(i);

phi2_scal = 1 - phi1(i);

F = @(C)

[-phi1_scal+(C(1)/(1-K(1,1)*C(1))^2)*(1+((V(1,1)*KAB*C(2))/(V(2,1)*(1-K(2,1)*C(2)))));-phi2_scal+(C(2)/(1-K(2,1)*C(2))^2)*(1+

((KAB*C(1))/(1-K(1,1)*C(1))))];

InitialGuess = [0.1;0.1];

Options = optimset('Display','iter');

XY = lsqnonlin(F,InitialGuess,0,1,Options)

TP(1,i) = XY(1);

TP(2,i) = XY(2);

phi=TP';

end

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