Sturm-Liouville eigenvalues calculation

Hallo,

I am trying to solve a Sturm-Liouville eigenvalues problem. From the Robin BC, I get the following trascendental equation for the variable x:

tan(x*L/(2*S)) = 4*x*tau*S/((x*tau)^2+(tau*c*V)^2-4*S^2),

where L, S, tau, c and V are parameters. I should have ideally infinite solution (I would like to compute the first 100 solutions), but I cannot find them. I was trying with fsolve:

F= @(x) tan(x/(2*S)*l)-4*x*S*tau/((x*tau)^2+(tau*c*V)^2-4*S^2);
for i=1:1:1000
    j = i-1;
    a(i) = j*1000;
    x0(i) = a(i);
    mu(i) = fsolve(F,x0(i));
end

but I don't manage. Do you have any idea?

Thank you in advance

[darova]

What is the problem? Can't you find a solution or what?

Answer 1

[Bjorn Gustavsson]

Have you checked the file-exchange contribution: discrete-orthogonal-polynomial. It solves this kind of problems numerically.