sym/subsindex error. fplot error.

I am trying to find all the numerical solutions to the equation while also plotting the function.

This is code:

syms k_f
h=4e-6;
k_0=2.*pi/10.^-6; 
n_g=1.5;
n_c=1.0;
n_s=1.4;
y_s=(k_0.^2.*(n_g.^2-n_s.^2)-k_f).^0.5;
y_c=(k_0.^2.*(n_g.^2-n_c.^2)-k_f).^0.5;
k_fmax=3383598.893;
num=k_f.*((n_g.^2/n_s.^2).*y_s+(n_g.^2/n_c.^2).*y_c);
dem=k_f.^2-((n_g.^4/(n_c.^2.*n_s.^2)).*(y_c.*y_s));
G=tan(h.*k_f)==num/dem;
beta=(k_0.^2.*n_g.^2-k_f.^2).^0.5;
for h=4.*10.^-6
    vpasolve(G,k_f,'Random',true)
end 
%S=vpasolve(G,k_f);
P=fplot(k_f,G);
grid on

And this is the result:

>> Homework_2_4B
 
ans =
 
3.4688567555791838811284939104133e-55
 
Error using sym/subsindex (line 855)
Invalid indexing or function definition. Indexing must follow MATLAB
indexing. Function arguments must be symbolic variables, and function
body must be sym expression.

Error in Homework_2_4B (line 17)
P=fplot(k_f,G);

Answer 1

[Walter Roberson]

P=fplot(k_f,G);

G is an equation, and k_f is a plain symbolic variable.

When you fplot() you need to put an expression to be plotted first. The second (optional) parameter is the range to plot over.

fplot([lhs(G)-rhs(G),0],[-1e-60 1e-60])

I am not seeing any solutions on the plots, other than the trivial solution at 0.

[Walter Roberson]

I spoke too soon. There is an upper bound of 11448741105263.7 after which the equation goes complex valued. There do appear to be non-trivial solutions, such as near 727603.7298 . You might need to increase your digits() to compute them.