How to solve error message in fsolve stating: "The vector of function values is near zero, as measured by the selected value of the function tolerance. However, the last step was ineffective"

Dear all, I am trying to solve transcendental equations of TM mode using fsolve, but I constantly get error message stating:

"The vector of function values is near zero, as measured by the selected value of the function tolerance. However, the last step was ineffective."

Here are the code and myfun fiels, please help me!

Thxs!

% Given:
close all; clear all;
mu_o = 4*pi*10^(-7); mu_r = 1;
esp_o = (10^(-9))/(36*pi); esp_r = 2.56;
esp_d = esp_o*esp_r;
mu_d = mu_o*mu_r;
h = 0.3175; % [cm]
f_c1 = 18.913e9; % from example 8-11 pp 17.
f = 0:f_c1/1000:2*f_c1;
b_z = 0; %Initialization 
for f_index = 1:1:length(f)
    w = (2*pi*f(f_index));
    b_z = 793; % Initial point guessing
    options = optimset('Display','iter','MaxFunEvals',1e20,'TolFun',1e-10,'TolX',1e-10);
    b_z_sol = fsolve(@myfun, b_z, options);
end
b_yd_sol = (sqrt(w.^2*mu_d*esp_d - b_z_sol.^2))/100; % [rad/cm] equ. 8-160c
a_sol = (sqrt(b_z_sol.^2 - (w.^2*mu_o*esp_o)))/100; % [rad/cm] equ. 8-160d
b_o = w*sqrt(mu_o*esp_o);
b_d = w*sqrt(mu_d*esp_d);
% Figure-a
subplot(2,1,1);
plot(f(f_index)/f_c1,real(b_z_sol));
hold on;
plot(f(f_index)/f_c1, real(b_yd_sol), ':');
plot(f(f_index)/f_c1, real(a_sol), '--');
hold off;
axis([0 f(f_index)/f_c1 0 9]);
xlabel('Normalized frequency (f/f_C_1)');
title('Attenuation and Phase Constants of TM^{Z}_m');
subplot(2,1,2);
% Figure-b
plot(b_o, w);
hold on;
plot(b_d, w);
plot(real(b_z_sol), w);
axis([0 13e2 0 2e11]);
xlabel('\beta_o \beta_z \beta_d');
ylabel('\omega(\beta_o \beta_z \beta_d)');
title('Dispersion Curve');
hold off;

% myfum.m file code:

function F = myfun(b_z)
global w;
mu_o = 4*pi*10^(-7); 
mu_r = 1;
esp_o = (10^(-9))/(36*pi);
esp_r = 2.56;
esp_d = esp_o*esp_r;
mu_d = mu_o*mu_r;
h = 0.3175; % [cm]
f_c1 = 18.913e9; % from example 8-11 pp 417
f = 0:18.913e6:2*f_c1; 
for f_index = 1:1:length(f)
end
w = (2*pi*f(f_index));
% Iteration equations for the three unknowns 
b_yd = (sqrt(w.^2*mu_d*esp_d - b_z.^2))/100; % [rad/cm] equ. 8-160c
a = (sqrt(b_z.^2 - (w.^2*mu_o*esp_o)))/100; % [rad/cm] equ. 8-160d
F = (a*(esp_d/esp_o)) - (b_yd*h*tan(b_yd*h)); % equ 8-160b 
end

[madhan ravi]

Please don’t close the question that have an answer becuase it will be deleted after 10 days if a question is closed.

[Kai Wang]

Hi, I think what you have plotted is a single point. You should let b_o, b_d and w to be a colume vector.

Answer 1

[Alan Weiss]

Without running your code, I can tell you that the exit message you give is NOT an error message. Read its first part:

"The vector of function values is near zero, as measured by the selected value of the function tolerance."

This means that fsolve found a solution. So I think that you should't worry about the second part of the message, which is about algorithm internals.

Alan Weiss

MATLAB mathematical toolbox documentation

[Yonas Gezahegn]

Thanks a lot Alan!

My problem is to plot a graph using the output results.

Can anyone can give me a hint please.

[Alan Weiss]

I don't understand what you want to plot. I suggest that you start a new question with some details.

Alan Weiss

MATLAB mathematical toolbox documentation