Sinc Function computation of the eigenvalues of Sturm-Liouville problems
The sinc function is defined by \(\sin c(t)=\sin (\pi t)/\pi t,\) \(t\in (- \infty,\infty)\). As one of the applications of this function, the authors develop a collocation scheme using sinc basis functions to approximate the eigenvalues of regular and singular Sturm-Liouville boundary value problems. Utilizing a conformal map of the given connected domain onto the infinite strip, the error in the approximation of the eigenvalues is shown to converge at the rate exp(-\(\alpha\sqrt{N})\) \((\alpha >0)\), where \(2N+1\) basis elements in the collocation scheme is used. A number of numerical test examples are included (for both finite and infinite interval) to indicate the accuracy and the implementation of the method.
scientific article; zbMATH DE number 4003408
scientific article