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Sturm-Liouville eigenvalues calculation

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Luigi Romano
Luigi Romano on 12 Jun 2020
Answered: Bjorn Gustavsson on 13 Jun 2020
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));
but I don't manage. Do you have any idea?
Thank you in advance
  1 Comment
darova on 13 Jun 2020
What is the problem? Can't you find a solution or what?

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Answers (1)

Bjorn Gustavsson
Bjorn Gustavsson on 13 Jun 2020
Have you checked the file-exchange contribution: discrete-orthogonal-polynomial. It solves this kind of problems numerically.

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