MATLAB: Error using trustnleqn (line 28) Objective function is returning undefined values at initial point. FSOLVE cannot continue.

fsolveMATLAB

I'm having trouble with my code, which is note that complicated. It looks like it's not converging. For a initial condition of [1,1] the result is: z =
-1.0322 - 0.1404i
 0.0678 + 0.0000i
But for other initial conditions i get this error: Error using trustnleqn (line 28) Objective function is returning undefined values at initial point. FSOLVE cannot continue.
Error in fsolve (line 388) trustnleqn(funfcn,x,verbosity,gradflag,options,defaultopt,f,JAC,…
Here's the code:
function F=myFunction(z)
hf_f = 40000000;
Cp = 1200;
phi = 1;
Yf_e = 1/(1+(16/phi));
YOx = (16/phi)/(1+(16/phi));
r = 0.04;
V = (4/3)*3.1415*r^3;
Tref = 298;
P = 1;
A = 1.1*10^12;
K = 15.098;
M = 29;
R = 8314;
m = 0.1;
n = 1.65;
m2=0.0011;
Ts = z(1);
Yf_s = z(2);
F(1)=(hf_f/Cp)*(Yf_e - Yf_s) + Tref - Ts;
F(2)=Yf_e - A*exp(K*Ts)*((Yf_s/M)^m)*((YOx*0.21/M)^n)*(((P*M)/(R*Ts))^(m+n))*(M*V/m2) - Yf_s;
end
Then I use
>> zg = [1;1];
>> z=fsolve(@myFunction,zg);
To call initial conditions and solve.
Any help is apreciated. Thank you!

Best Answer

For the original version of the function, there appear to be an infinite number of solutions spaced approximately 3/1509800 /2 apart in the imaginary plane, with real component 57599/850000 . For example one solution is at approximately
57599/850000 -245788448974313916824885/24556871395725172650816064*1i
With the solutions being roughly 1E-6 apart, you would need to use quite fine tolerances on the fsolve to get convergence.
For the revised version, the solutions appear to be closer than 1/100000 apart in the imaginary plane.
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