Computing eigenvalues of the string by sampling

AbstractIn this paper, we shall use the Shannon-Whittacker-Kotelnikov sampling theorem to approximate the eigenvalues of the string, y″(t) + μ2w(t)y(t) = 0, where the weight w(t) ≥ 0 is allowed to vanish on subintervals. After a discussion on the truncation error, numerical results are provided