a system of non-linear equations (using fsolve in a loop)

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Hi friends,
I am trying to solve a system of equations of 5 equations and 5 variables. Equations are non-linear ( containing quadratic function, sine, and cosine functions).
How can I change some of the equation parameters ( b1, b2, b3, g1, g2, g3 in terms of n , m) ,using a loop, and solve the system of equations by "fsolve" each time?
My code is as following but there is an error as: "Unrecognized function or variable 'n' ". what should I do now???
How should I introduce n, m to both m-files?? Where should I apply the for- loop?
Thanks for your guides in advance.
function G= fsolve_trial(X)
% Parameters:%
k1 = 0.25; k2 = 0.5; k3 = 0.2;
Lx = 40e-03;
Ly = 40e-03;
Lz1 = 0.08e-03; Lz2 = 2e-03; Lz3 = 10e-03;
a1 = 5.79e-08; a2 = 1.23e-07; a3 = 6.67e-08;
b1 = (n*pi/Lx)^2;
b2 = (n*pi/Lx)^2;
b3 = (n*pi/Lx)^2;
g1 = (m*pi/Ly)^2;
g2 = (m*pi/Ly)^2;
g3 = (m*pi/Ly)^2;
w1 = 0; w2 = 101; w3 = 137;
% Variable Vector:%
s1= X(1);
s2= X(2);
s3= X(3);
s21= X(4);
s32= X(5);
% Equations:%
eq1=k2*k3*s21*s32*cos(Lz1*s1)*cos(Lz2*((a1*s1^2 + a1*b1 - a2*b2 + a1*g1 - a2*g2 + a1*w1 - a2*w2)/a2)^(1/2))*cos(Lz3*((a1*s1^2 + a1*b1 - a3*b3 + a1*g1 - a3*g3 + a1*w1 - a3*w3)/a3)^(1/2)) - k2*s21*cos(Lz1*s1)*sin(Lz2*((a1*s1^2 + a1*b1 - a2*b2 + a1*g1 - a2*g2 + a1*w1 - a2*w2)/a2)^(1/2))*sin(Lz3*((a1*s1^2 + a1*b1 - a3*b3 + a1*g1 - a3*g3 + a1*w1 - a3*w3)/a3)^(1/2)) - k3*s32*cos(Lz3*((a1*s1^2 + a1*b1 - a3*b3 + a1*g1 - a3*g3 + a1*w1 - a3*w3)/a3)^(1/2))*sin(Lz1*s1)*sin(Lz2*((a1*s1^2 + a1*b1 - a2*b2 + a1*g1 - a2*g2 + a1*w1 - a2*w2)/a2)^(1/2)) - cos(Lz2*((a1*s1^2 + a1*b1 - a2*b2 + a1*g1 - a2*g2 + a1*w1 - a2*w2)/a2)^(1/2))*sin(Lz1*s1)*sin(Lz3*((a1*s1^2 + a1*b1 - a3*b3 + a1*g1 - a3*g3 + a1*w1 - a3*w3)/a3)^(1/2));
eq2= s2-sqrt((a1/a2)*(b1+g1+s1^2+w1)-(b2+g2+w2));
eq3= s3-sqrt((a1/a3)*(b1+g1+s1^2+w1)-(b3+g3+w3));
eq4= s21- (s2/s1);
eq5= s32- (s3/s2);
G= [eq1; eq2; eq3; eq4; eq5];
%%%%%%%%%%%%%%%%%%%%
And:
% Crating Solved Variable Matrix: %
ss1= zeros(10, 10);
ss2= zeros(10, 10);
ss3= zeros(10, 10);
for n=1:10
for m=1:10
fhandle= @fsolve_trial;
X0= [120 12 100 0.1 8];
X= fsolve( fhandle, X0);
ss1(n,m)=X(1);
ss2(n,m)=X(2);
ss3(n,m)=X(3);
end
end

Accepted Answer

Star Strider
Star Strider on 30 Apr 2021
Edited: Star Strider on 30 Apr 2021
Pass them as extra parameters. See Passing Extra Parameters for details.
This appears to work —
% Crating Solved Variable Matrix: %
ss1= zeros(10, 10);
ss2= zeros(10, 10);
ss3= zeros(10, 10);
for n=1:10
for m=1:10
fhandle= @(X)fsolve_trial(X,n,m);
X0= [120 12 100 0.1 8];
X = fsolve( fhandle, X0);
ss1(n,m)=X(1);
ss2(n,m)=X(2);
ss3(n,m)=X(3);
end
end
Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Solver stopped prematurely. fsolve stopped because it exceeded the iteration limit, options.MaxIterations = 4.000000e+02. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient. Equation solved, inaccuracy possible. The vector of function values is near zero, as measured by the value of the function tolerance. However, the last step was ineffective.
ss1
ss1 =
1.0e+02 * 1.4043 + 0.0000i 1.7696 + 0.0000i 2.2220 + 0.0000i 2.1548 + 0.0000i 3.0841 + 0.0000i 2.4868 + 0.0000i 2.9175 + 0.0000i 3.9615 + 0.0000i 4.2005 + 0.0000i 3.0797 + 0.0000i 1.7696 + 0.0000i 2.0579 + 0.0000i 2.4366 + 0.0000i 2.8305 + 0.0000i 2.1634 + 0.0000i 3.1982 + 0.0000i 3.7637 + 0.0000i 4.0065 + 0.0000i 2.8257 + 0.0000i 3.1251 + 0.0000i 2.2220 + 0.0000i 2.4366 + 0.0000i 2.7306 + 0.0000i 3.0460 + 0.0000i 2.4983 + 0.0000i 3.1816 + 0.0000i 3.8501 + 0.0000i 4.0785 + 0.0000i 4.3026 + 0.0000i 3.1992 + 0.0000i 2.1548 + 0.0000i 2.8305 + 0.0000i 3.0460 + 0.0000i 2.5124 + 0.0000i 3.2059 + 0.0000i 3.7456 + 0.0000i 3.9615 + 0.0000i 2.7415 + 0.0000i 4.3879 + 0.0000i 4.6057 + 0.0000i 3.0841 + 0.0000i 2.1634 + 0.0000i 2.4983 + 0.0000i 3.2059 + 0.0000i 2.9175 + 0.0000i 3.8991 + 0.0000i 4.0925 + 0.0000i 4.2901 + 0.0000i 3.1549 + 0.0000i 4.7031 + 0.0000i 2.4868 + 0.0000i 3.1982 + 0.0000i 3.1816 + 0.0000i 3.7456 + 0.0000i 3.8991 + 0.0000i 4.0643 + 0.0000i 2.8257 + 0.0000i 3.0645 + 0.0000i 3.3143 + 0.0000i 4.8183 + 0.0000i 2.9175 + 0.0000i 3.7637 + 0.0000i 3.8501 + 0.0000i 3.9615 + 0.0000i 4.0925 + 0.0000i 2.8257 + 0.0000i 4.3999 + 0.0000i 4.5724 + 0.0000i 3.4934 + 0.0000i 4.9497 + 0.0000i 3.9615 + 0.0000i 4.0065 + 0.0000i 4.0785 + 0.0000i 2.7415 + 0.0000i 4.2901 + 0.0000i 3.0645 + 0.0000i 4.5724 + 0.0000i 4.7383 + 0.0000i 4.9098 + 0.0000i 5.0957 + 0.0000i 4.2005 + 0.0000i 2.8257 + 0.0000i 4.3026 + 0.0000i 4.3879 + 0.0000i 3.1549 + 0.0000i 3.3143 + 0.0000i 3.4934 + 0.0000i 4.9098 + 0.0000i 5.0766 + 0.0000i 5.2551 + 0.0000i 3.0797 + 0.0000i 3.1251 + 0.0000i 3.1992 + 0.0000i 4.6057 + 0.0000i 4.7031 + 0.0000i 4.8183 + 0.0000i 4.9497 + 0.0000i 5.0957 + 0.0000i 5.2551 + 0.0000i 5.4269 + 0.0000i
ss2
ss2 =
1.0e+02 * 0.5151 + 0.0000i 0.0000 + 0.4103i 0.0000 + 0.9751i 0.0005 + 1.8378i 0.0000 + 2.0053i 0.0121 + 2.9317i 0.0865 + 3.1562i 0.0000 + 3.7207i -0.0000 + 4.2983i -0.0000 + 5.3404i 0.0000 + 0.4103i 0.0000 + 0.7927i 0.0000 + 1.2081i 0.0000 + 1.6638i 0.0031 + 2.6908i 0.0871 + 2.5576i 0.0000 + 3.2627i 0.0000 + 3.8281i -0.0000 + 4.8992i -0.0000 + 5.4191i 0.0000 + 0.9751i 0.0000 + 1.2081i 0.0000 + 1.5417i 0.0000 + 1.9505i 0.0017 + 2.7808i 0.0992 + 2.7331i 0.0000 + 3.4595i 0.0000 + 4.0016i 0.0000 + 4.5474i -0.0000 + 5.5478i 0.0005 + 1.8378i 0.0000 + 1.6638i 0.0000 + 1.9505i -0.0050 + 2.6887i 0.0874 + 2.5754i 0.0000 + 3.2222i 0.0000 + 3.7207i -0.0000 + 4.7529i 0.0000 + 4.7555i 0.0000 + 5.2817i 0.0000 + 2.0053i 0.0031 + 2.6908i 0.0017 + 2.7808i 0.0874 + 2.5754i 0.0865 + 3.1562i 0.0000 + 3.5734i 0.0000 + 4.0355i 0.0000 + 4.5170i -0.0000 + 5.4710i 0.0000 + 5.5143i 0.0121 + 2.9317i 0.0871 + 2.5576i 0.0992 + 2.7331i 0.0000 + 3.2222i 0.0000 + 3.5734i 0.0000 + 3.9674i -0.0000 + 4.8992i -0.0000 + 5.3139i -0.0000 + 5.7478i 0.0000 + 5.7864i 0.0865 + 3.1562i 0.0000 + 3.2627i 0.0000 + 3.4595i 0.0000 + 3.7207i 0.0000 + 4.0355i -0.0000 + 4.8992i 0.0000 + 4.7846i 0.0000 + 5.2020i -0.0000 + 6.0587i 0.0000 + 6.0929i 0.0000 + 3.7207i 0.0000 + 3.8281i 0.0000 + 4.0016i -0.0000 + 4.7529i 0.0000 + 4.5170i -0.0000 + 5.3139i 0.0000 + 5.2020i 0.0004 + 5.5895i 0.0000 + 6.0002i 0.0000 + 6.4288i -0.0000 + 4.2983i -0.0000 + 4.8992i 0.0000 + 4.5474i 0.0000 + 4.7555i -0.0000 + 5.4710i -0.0000 + 5.7478i -0.0000 + 6.0587i 0.0000 + 6.0002i 0.0000 + 6.3850i 0.0000 + 6.7899i -0.0000 + 5.3404i -0.0000 + 5.4191i -0.0000 + 5.5478i 0.0000 + 5.2817i 0.0000 + 5.5143i 0.0000 + 5.7864i 0.0000 + 6.0929i 0.0000 + 6.4288i 0.0000 + 6.7899i 0.0000 + 7.1723i
ss3
ss3 =
1.0e+02 * 1.2391 + 0.0000i 1.5158 + 0.0000i 1.8596 + 0.0000i 1.6232 - 0.0002i 2.4753 + 0.0000i 1.5393 - 0.0791i 1.5978 - 0.0767i 2.8843 + 0.0000i 2.9376 - 0.0000i 0.0002 + 0.0001i 1.5158 + 0.0000i 1.7354 + 0.0000i 2.0204 + 0.0000i 2.3051 + 0.0000i 1.2876 - 0.0392i 1.8964 - 0.6008i 2.8231 + 0.0000i 2.8959 + 0.0000i 0.0001 + 0.0002i 0.0002 + 0.0000i 1.8596 + 0.0000i 2.0204 + 0.0000i 2.2347 + 0.0000i 2.4507 + 0.0000i 1.6632 - 0.1738i 1.6083 - 0.5041i 2.8520 + 0.0000i 2.9129 + 0.0000i 2.9549 + 0.0000i 0.0002 + 0.0000i 1.6232 - 0.0002i 2.3051 + 0.0000i 2.4507 + 0.0000i 1.7473 - 0.2232i 1.8318 - 0.6176i 2.8166 + 0.0000i 2.8843 + 0.0000i 0.0002 + 0.0000i 2.9675 + 0.0000i 2.9932 + 0.0000i 2.4753 + 0.0000i 1.2876 - 0.0392i 1.6632 - 0.1738i 1.8318 - 0.6176i 1.5978 - 0.0767i 2.8669 + 0.0000i 2.9159 + 0.0000i 2.9529 + 0.0000i 0.0002 + 0.0000i 3.0024 + 0.0000i 1.5393 - 0.0791i 1.8964 - 0.6008i 1.6083 - 0.5041i 2.8166 + 0.0000i 2.8669 + 0.0000i 2.9097 + 0.0000i 0.0001 + 0.0002i 0.0002 + 0.0001i 0.0002 + 0.0001i 3.0119 + 0.0000i 1.5978 - 0.0767i 2.8231 + 0.0000i 2.8520 + 0.0000i 2.8843 + 0.0000i 2.9159 + 0.0000i 0.0001 + 0.0002i 2.9691 + 0.0000i 2.9898 + 0.0000i 0.0001 + 0.0003i 3.0211 + 0.0000i 2.8843 + 0.0000i 2.8959 + 0.0000i 2.9129 + 0.0000i 0.0002 + 0.0000i 2.9529 + 0.0000i 0.0002 + 0.0001i 2.9898 + 0.0000i 3.0115 - 0.0007i 3.0185 + 0.0000i 3.0298 + 0.0000i 2.9376 - 0.0000i 0.0001 + 0.0002i 2.9549 + 0.0000i 2.9675 + 0.0000i 0.0002 + 0.0000i 0.0002 + 0.0001i 0.0001 + 0.0003i 3.0185 + 0.0000i 3.0288 + 0.0000i 3.0379 + 0.0000i 0.0002 + 0.0001i 0.0002 + 0.0000i 0.0002 + 0.0000i 2.9932 + 0.0000i 3.0024 + 0.0000i 3.0119 + 0.0000i 3.0211 + 0.0000i 3.0298 + 0.0000i 3.0379 + 0.0000i 3.0456 - 0.0000i
function G= fsolve_trial(X,n,m)
% Parameters:%
k1 = 0.25; k2 = 0.5; k3 = 0.2;
Lx = 40e-03;
Ly = 40e-03;
Lz1 = 0.08e-03; Lz2 = 2e-03; Lz3 = 10e-03;
a1 = 5.79e-08; a2 = 1.23e-07; a3 = 6.67e-08;
b1 = (n*pi/Lx)^2;
b2 = (n*pi/Lx)^2;
b3 = (n*pi/Lx)^2;
g1 = (m*pi/Ly)^2;
g2 = (m*pi/Ly)^2;
g3 = (m*pi/Ly)^2;
w1 = 0; w2 = 101; w3 = 137;
% Variable Vector:%
s1= X(1);
s2= X(2);
s3= X(3);
s21= X(4);
s32= X(5);
% Equations:%
eq1=k2*k3*s21*s32*cos(Lz1*s1)*cos(Lz2*((a1*s1^2 + a1*b1 - a2*b2 + a1*g1 - a2*g2 + a1*w1 - a2*w2)/a2)^(1/2))*cos(Lz3*((a1*s1^2 + a1*b1 - a3*b3 + a1*g1 - a3*g3 + a1*w1 - a3*w3)/a3)^(1/2)) - k2*s21*cos(Lz1*s1)*sin(Lz2*((a1*s1^2 + a1*b1 - a2*b2 + a1*g1 - a2*g2 + a1*w1 - a2*w2)/a2)^(1/2))*sin(Lz3*((a1*s1^2 + a1*b1 - a3*b3 + a1*g1 - a3*g3 + a1*w1 - a3*w3)/a3)^(1/2)) - k3*s32*cos(Lz3*((a1*s1^2 + a1*b1 - a3*b3 + a1*g1 - a3*g3 + a1*w1 - a3*w3)/a3)^(1/2))*sin(Lz1*s1)*sin(Lz2*((a1*s1^2 + a1*b1 - a2*b2 + a1*g1 - a2*g2 + a1*w1 - a2*w2)/a2)^(1/2)) - cos(Lz2*((a1*s1^2 + a1*b1 - a2*b2 + a1*g1 - a2*g2 + a1*w1 - a2*w2)/a2)^(1/2))*sin(Lz1*s1)*sin(Lz3*((a1*s1^2 + a1*b1 - a3*b3 + a1*g1 - a3*g3 + a1*w1 - a3*w3)/a3)^(1/2));
eq2= s2-sqrt((a1/a2)*(b1+g1+s1^2+w1)-(b2+g2+w2));
eq3= s3-sqrt((a1/a3)*(b1+g1+s1^2+w1)-(b3+g3+w3));
eq4= s21- (s2/s1);
eq5= s32- (s3/s2);
G= [eq1; eq2; eq3; eq4; eq5];
%%%%%%%%%%%%%%%%%%%%
end
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More Answers (1)

Mahsa Babaee
Mahsa Babaee on 30 Apr 2021
Edited: Mahsa Babaee on 30 Apr 2021
Thank you so much for your help.
I pasted what you wrote , unfortunately still there is an error as:
>> trial_MatlabSite
Error using fsolve_trial
Too many input arguments.
Error in trial_MatlabSite>@(X)fsolve_trial(X,n,m) (line 10)
fhandle= @(X)fsolve_trial(X,n,m);
Error in fsolve (line 258)
fuser = feval(funfcn{3},x,varargin{:});
Error in trial_MatlabSite (line 12)
X = fsolve( fhandle, X0);
Caused by:
Failure in initial objective function evaluation. FSOLVE cannot continue.
I dont know what is wrong!
  4 Comments
Star Strider
Star Strider on 30 Apr 2021
My pleasure!
That was a way to test the code, and should not have been included in the code I posted. (I have now deleted it.)
If my Answer helped you solve your problem, please Accept it!
.

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