Problem with the fsolve function in MatLab

This is the function I try using for determining both CA0 and CB0

function F = root2d(x)
T12 = 22 + 273.15;
R = 8.314;

k1 = 74900*exp(-8050/(R*T12));

xA1 = 0.788;
xA2 = 0.974;
xA0 = 0;

t1 = 30;
t2 = 120;

%x(1) = CA0
%x(2) = CB0 

F(1) = (2*log(1-xA1) - 2 * log(-x(1)*xA1 + 2*x(2))) - (2*log(1-xA0) - 2 * log(2*x(2))) - k1*t1*(x(2)-2*x(1));
F(2) = (2*log(1-xA2) - 2 * log(-x(1)*xA2 + 2*x(2))) - (2*log(1-xA0) - 2 * log(2*x(2))) - k1*t2*(x(2)-2*x(1));

end

Then I input it in this program:

fun = @root2d

x0 = [0,0];
x = fsolve(fun,x0)

disp(x)

Can someone help with what is going wrong here?

Why the problem can't be solved?

May it be related to the values [0,0]?

Because if both of them are 0 at the same time the equation can't be solved.

Thanks everyone in advance!

[Walter Roberson]

Yes, you will need to use a different initial conditon.

Also you will probably need to use an options structure to increase the iterations limit.

Answer 1

[Walter Roberson]

fsolve can solve the system, but it requires that the second x input be between about 5e-6 and 1.1e-5 . Smaller values will lead to complex solutions; larger values will lead to no solution with the results not being even remotely close.