A SYMMETRICAL FINITE-DIFFERENCE METHOD FOR COMPUTING EIGENVALUES OF STURM-LIOUVILLE PROBLEMS

For computing eigenvalues of Sturm-Liouville problems by finite differ ence 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 symmetri c five-diagonal generalized matrix eigenvalue problem; under suitable conditions, it is shown to provide real and non-negative approximation s for eigenvalues of Sturm-Liouville problems with order three converg ence.