The code below runs nonstop, and the results are not shown. why is that?

syms J1 J5 J6 J7 Jm T1 T2 T3 T4 T5 T6 Tm
    %Jm = 1000; %5077.12;
    Js = 301.32;
    Je = 7;%330.136;
    A2 = 449200;
    A4 = 519000;
    Fms = 0.305;
    Fm1 = 0.45;
    Fme = 0.245;
    F1s = 0.610;
    F1m = 0.389;
    eps = 0.85;
    Te = 215;
 K1 = 60; %solar cell
 L1 = 0.2e-3; %solar cell
    R1 = 0.6e-4;
    K2 = 15; %solar panel
    L2 = 0.03; %solar panel
    F5e = 0.1;
    F5s = 0.03;
    Fem = 0.1;
    Fe5 = 0.01;

    S0 = -Jm + eps*5.67e-8*Tm^4 + ((1-eps)*5*1360);
    S1 = -(5.67e-8*Tm^4 - Jm)*(A2*eps)/(1-eps) + (Jm - Js)*(A2*Fms) + (Jm - J1)*(A2*Fm1) + (Jm - Je)*(A2*Fme);%J1
    S2 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (J1 - Js)*(A4*F1s) + (J1 - Jm)*(A4*F1m);%T1
    S3 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (T1-T2)*K1*A4/L1;%T2
    S4 = -(T1 - T2)*K1/L1 + (T2-T3)/R1;
    S5 = -(T2-T3)/R1 + (T3-T4)/L2*K2;
    S6 = -(T3 - T4)/L2*K2 + (5.67e-8*T4^4 - J6)*A4*eps/(1-eps);
    S7 = -(5.67e-8*T4^4 - J6)*eps/(1-eps) + (J6 - J7);
    S8 = -(J6-J7) + (5.67e-8*T5^4 - J7)*eps/(1-eps) - 185.95;
    S9 = -(5.67e-8*T5^4 - J7)*eps/(1-eps) + (T5 - T6)*K2/L2;
    S10 = -(5.67e-8*T6^4 - J5)*eps/(1-eps) + (J5 - Je)*F5e + (J5 - J1)*F5s;
    S11 = -(5.67e-8*Te^4 - Je)*eps/(1-eps) + (Je - Jm)*Fem + (Je- J5)*Fe5;

S = [S0,S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11];
vars = [J1, J5, J6, J7, Jm, T1, T2, T3, T4, T5, T6, Tm];

sol = solve(S, vars);
T1_val = real(double(sol.T1(1)))
T2_val = real(double(sol.T2(1)))
T3_val = real(double(sol.T3(1)))
T4_val = real(double(sol.T4(1)))
T5_val = real(double(sol.T5(1)))
T6_val = real(double(sol.T6(1)))

Answer 1

[Torsten]

The code below runs nonstop, and the results are not shown. why is that?

"solve" won't succeed for your system of equations because it is too complicated. Try the numerical solver "fsolve" instead. I hope you know better initial guesses for the solution variables than just random values.

x0 = rand(12,1);
options = optimset('MaxIter',300000,'MaxFunEvals',300000);
x = fsolve(@(x)fun(x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10),x(11),x(12)),x0,options)

Solver stopped prematurely.

fsolve stopped because it exceeded the function evaluation limit,
options.MaxFunctionEvaluations = 3.000000e+05.

x = 12x1

3.9894 0.0280 0.7814 0.3784 1.2731 0.0304 0.0305 0.0546 -0.0699 8.1945

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function res = fun(J1,J5, J6, J7, Jm, T1, T2, T3, T4, T5, T6, Tm)
    %Jm = 1000; %5077.12;
    Js = 301.32;
    Je = 7;%330.136;
    A2 = 449200;
    A4 = 519000;
    Fms = 0.305;
    Fm1 = 0.45;
    Fme = 0.245;
    F1s = 0.610;
    F1m = 0.389;
    eps = 0.85;
    Te = 215;
 K1 = 60; %solar cell
 L1 = 0.2e-3; %solar cell
    R1 = 0.6e-4;
    K2 = 15; %solar panel
    L2 = 0.03; %solar panel
    F5e = 0.1;
    F5s = 0.03;
    Fem = 0.1;
    Fe5 = 0.01;
    S0 = -Jm + eps*5.67e-8*Tm^4 + ((1-eps)*5*1360);
    S1 = -(5.67e-8*Tm^4 - Jm)*(A2*eps)/(1-eps) + (Jm - Js)*(A2*Fms) + (Jm - J1)*(A2*Fm1) + (Jm - Je)*(A2*Fme);%J1
    S2 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (J1 - Js)*(A4*F1s) + (J1 - Jm)*(A4*F1m);%T1
    S3 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (T1-T2)*K1*A4/L1;%T2
    S4 = -(T1 - T2)*K1/L1 + (T2-T3)/R1;
    S5 = -(T2-T3)/R1 + (T3-T4)/L2*K2;
    S6 = -(T3 - T4)/L2*K2 + (5.67e-8*T4^4 - J6)*A4*eps/(1-eps);
    S7 = -(5.67e-8*T4^4 - J6)*eps/(1-eps) + (J6 - J7);
    S8 = -(J6-J7) + (5.67e-8*T5^4 - J7)*eps/(1-eps) - 185.95;
    S9 = -(5.67e-8*T5^4 - J7)*eps/(1-eps) + (T5 - T6)*K2/L2;
    S10 = -(5.67e-8*T6^4 - J5)*eps/(1-eps) + (J5 - Je)*F5e + (J5 - J1)*F5s;
    S11 = -(5.67e-8*Te^4 - Je)*eps/(1-eps) + (Je - Jm)*Fem + (Je- J5)*Fe5;
    res = [S0;S1;S2;S3;S4;S5;S6;S7;S8;S9;S10;S11];
    end

[Ghanim]

Thanks for your suggestion. I have updated the initial gusess and incraesed the tolorence to 3e7. It takes like 5 minutes to run and the following error occures:

Solver stopped prematurely.

fsolve stopped because it exceeded the function evaluation limit,options.MaxFunctionEvaluations = 3.000000e+07.

Increseing the tolerence more keeps Matlab running nonstop.

My code is as follow:

% Define the function representing the system of equations

   Js = 301.32;
    Je = 7;%330.136;
    A2 = 449200;
    A4 = 519000;
    Fms = 0.305;
    Fm1 = 0.45;
    Fme = 0.245;
    F1s = 0.610;
    F1m = 0.389;
    eps = 0.85;
    Te = 215;
 K1 = 60; %solar cell
 L1 = 0.2e-3; %solar cell
    R1 = 0.6e-4;
    K2 = 15; %solar panel
    L2 = 0.03; %solar panel
    F5e = 0.1;
    F5s = 0.03;
    Fem = 0.1;
    Fe5 = 0.01;
fun = @(x) [
    -x(1) + eps*5.67e-8*x(2)^4 + ((1-eps)*5*1360);
    -(5.67e-8*x(2)^4 - x(1))*(A2*eps)/(1-eps) + (x(1) - Js)*(A2*Fms) + (x(1) - x(3))*(A2*Fm1) + (x(1) - Je)*(A2*Fme);
    -(5.67e-8*x(4)^4 - x(3))*(A4*eps)/(1-eps) + (x(3) - Js)*(A4*F1s) + (x(3) - x(1))*(A4*F1m);
    -(5.67e-8*x(4)^4 - x(3))*(A4*eps)/(1-eps) + (x(4)-x(5))*K1*A4/L1;
    -(x(4) - x(5))*K1/L1 + (x(5)-x(6))/R1;
    -(x(5) - x(6))/R1 + (x(6)-x(7))/L2*K2;
    -(x(6) - x(7))/L2*K2 + (5.67e-8*x(7)^4 - x(8))*A4*eps/(1-eps);
    -(5.67e-8*x(7)^4 - x(8))*eps/(1-eps) + (x(8) - x(9));
    -(x(8)-x(9)) + (5.67e-8*x(10)^4 - x(9))*eps/(1-eps) - 185.95;
    -(5.67e-8*x(10)^4 - x(9))*eps/(1-eps) + (x(10) - x(11))*K2/L2;
    -(5.67e-8*x(11)^4 - x(12))*eps/(1-eps) + (x(12) - Je)*F5e + (x(12) - x(3))*F5s;
    -(5.67e-8*Te^4 - Je)*eps/(1-eps) + (Je - x(1))*Fem + (Je- x(12))*Fe5
];


% Initial guess for the solution
x0 = [4000; 400; 4000; 450; 450; 420; 400; 4000; 4000; 400; 390; 4000];

options = optimset('MaxIter',30000000,'MaxFunEvals',30000000);

% Solve the system of equations
x = fsolve(fun, x0, options);

[Torsten]

I cannot help the solver to converge. As said, it's up to you to choose good initial guesses for the unknowns and to check the equations for possible errors or unrealistic parameter settings.

[Ghanim]

I found some errors with the equations and the modifed code is below. A new error appears as follow:

"Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm instead. > In fsolve (line 348)

In SS2 (line 50)

No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,

but the vector of function values is not near zero as measured by the

value of the function tolerance.

<stopping criteria details>

fsolve stopped because the sum of squared function values, r, has gradient with relative

norm 8.408653e-13; this is less than 1e-4*options.OptimalityTolerance = 1.000000e-10.

However, r = 1.335682e+06, exceeds sqrt(options.FunctionTolerance) = 1.000000e-03."

% Define the function representing the system of equations

   Js = 301.32;
    Je = 7;%330.136;
    A2 = 449200;
    A4 = 519000;
    Fms = 0.305;
    Fm1 = 0.45;
    Fme = 0.245;
    F1s = 0.610;
    F1m = 0.389;
    eps = 0.85;
    Te = 215;
 K1 = 60; %solar cell
 L1 = 0.2e-3; %solar cell
    R1 = 0.6e-4;
    K2 = 15; %solar panel
    L2 = 0.03; %solar panel
    F5e = 0.1;
    F5s = 0.03;
    Fem = 0.1;
    Fe5 = 0.01;
fun = @(x) [
    -x(1) + eps*5.67e-8*x(2)^4 + ((1-eps)*5*1360);
    -(5.67e-8*x(2)^4 - x(1))*eps/(1-eps) + (x(1) - Js)*Fms + (x(3) - x(1))*F1m + (x(1) - Je)*Fme;
    -(x(3) - 5.67e-8*x(4)^4)*eps/(1-eps) + (x(3) - Js)*F1s + (x(3) - x(1))*F1m;
    -(x(3) - 5.67e-8*x(4)^4)*eps/(1-eps) + (x(4)-x(5))*K1/L1;
    -(x(4) - x(5))*K1/L1 + (x(5)-x(6))/R1;
    -(x(5) - x(6))/R1 + (x(6)-x(7))/L2*K2;
    -(x(6) - x(7))/L2*K2 + (5.67e-8*x(7)^4 - x(8))*eps/(1-eps);
    -(5.67e-8*x(7)^4 - x(8))*eps/(1-eps) + (x(8) - x(9));
    -(x(8)-x(9)) + (5.67e-8*x(10)^4 - x(9))*eps/(1-eps) - 185.95;
    -(5.67e-8*x(10)^4 - x(9))*eps/(1-eps) + (x(10) - x(11))*K2/L2;
    -(x(10) - x(11))*K2/L2 + (5.67e-8*x(11)^4 - x(12))*eps/(1-eps);
    -(5.67e-8*x(11)^4 - x(12))*eps/(1-eps) + (x(12) - Je)*F5e + (x(12) - x(3))*F5s;
    -(5.67e-8*Te^4 - Je)*eps/(1-eps) + (Je - x(1))*Fem + (Je- x(12))*Fe5;
];


% Initial guess for the solution
x0 = [4000; 400; 4000; 450; 450; 420; 400; 4000; 4000; 400; 390; 4000];

options.StepTolerance = 1e-15;

%options = optimset('MaxIter',40000,'MaxFunEvals',40000);

%options = optimoptions('fsolve','Display','iter');

% Solve the system of equations
x = fsolve(fun, x0, options);

[Torsten]

You specify 13 equations for 12 unknowns. Usually, such a system is unsolvable and only permits as least-squares solution.