New numerical algorithms for eigenvalues and eigenvectors of second order differential equations

Abstract

In this paper we present for the first time an accurate, fast, and easy to implement numerical algorithm to find the eigenvalues and eigenvectors of the equation L(x;λ) = (rx')'+ px + λqx = 0. These ideas follow from a theory of quadratic forms given by the first author and will be applicable in a wide variety of eigenvalue problems. We include test runs to demonstrate that the accuracy of our methods are superior to more conventional projection methods