A symmetric finite difference method for computing eigenvalues of Sturm-Liouville problems

AbstractFor computing eigenvalues of Sturm-Liouville problems by finite difference methods, Usmani [1] described several methods, but the order of a symmetric method could not exceed two. It is therefore natural to ask if a higher order symmetric method can be found. In the present paper, we describe a new finite difference method which leads to a symmetric five-diagonal generalized matrix eigenvalue problem; under suitable conditions, it is shown to provide real and non-negative approximations for eigenvalues of Sturm-Liouville problems with order three convergence