Computing eigenvalues of Sturm–Liouville problems by Hermite interpolations

Abstract

We establish a new method to compute the eigenvalues of Sturm---Liouville problems by the use of Hermite interpolations at equidistant nodes. We rigorously give estimates for the error by considering both truncation and amplitude errors. We compare the results of the new technique with those involving the classical sinc method as well as a SLEIGN2-based method. We also introduce curves that illustrate the enclosure intervals.