fsolve no solution found

Dear all, I have a system of non-linear equations that needs to be solved. I have read some articles from Matlab to improve the performance of fsolve but alas, it hasn't been successful.

Could you please help me? Thanks

P/S: the general curves of alpha and beta look actually quite right (I'm not sure about the quantity) except the fact that there is a small peak at element 570. I would expect a smooth curve there so I think it's because of the no solution found from fsolve.

The code is as follows:

close all
clear all
clc
load('Data.mat')
x0=[pi;0];
for m=1:1:length(w_vector)
    w=w_vector(m);

      options = optimoptions('fsolve','Display','iter','Algorithm','levenberg-marquardt','ScaleProblem','jacobian','MaxFunctionEvaluations',2000,'MaxIterations',1500,'OptimalityTolerance',1e-12,'FunctionTolerance',1e-20,'StepTolerance',1e-12);
      F_med = @(x) [real(k1_l)*cosh(x(1))*cos(x(2))-imag(k1_l)*sinh(x(1))*sin(x(2))+real(k2_l)*cosh(2*x(1))*cos(2*x(2))-imag(k2_l)*sinh(2*x(1))*sin(2*x(2))+real(k3_l)*cosh(3*x(1))*cos(3*x(2))-imag(k3_l)*sinh(3*x(1))*sin(3*x(2))-(w0/w)^2+1+real(L1_l(m)/L);...
                real(k1_l)*sinh(x(1))*sin(x(2))+imag(k1_l)*cosh(x(1))*cos(x(2))+real(k2_l)*sinh(2*x(1))*sin(2*x(2))+imag(k2_l)*cosh(2*x(1))*cos(2*x(2))+real(k3_l)*sinh(3*x(1))*sin(3*x(2))+imag(k3_l)*cosh(3*x(1))*cos(3*x(2))-(1/Q)*(w0/w)+imag(L1_l(m)/L)];
      [x,fval] = fsolve(F_med,x0,options);
      alpha(m)=x(1);
      beta(m)=x(2);
      x0 = [x(1);x(2)];
  end
figure
hold on
plot(alpha,'r','Linewidth',3)
plot(beta,'b--','Linewidth',3)
axis tight square
grid on
set(findall(gcf,'-property','FontName'),'FontName', 'Times New Roman','fontsize',22)

[Walter Roberson]

x0 is needed for the fsolve() call, but is not defined in your code and is not part of the .mat file.

[Shan Chu]

Hi, X0=[pi;0];

I also corrected the question

Answer 1

[Walter Roberson]

You are trying to solve a system of 2 x 1001 equations in two variables, simultaneously, because your equation is in terms of the k* variables that are 1 x 1001.

Perhaps you want to loop over corresponding k* variables.