Sturm results on oscillation and comparison for solutions of a second-order differential equation have a topological nature in their own. Roughly speaking they describe the rotation of a straight line in the phase plane of the equation. Many generalization of this results were obtained; among the others we recall the symplectic version due to Arnol’d in [2] for second order hamiltonian systems ...

In this study, we suggest an efficient and useful method by using Chebyshev polynomials to approximate eigenvalues of a non-singular sixth-order Sturm-Liouville equation. This method uses Chebyshev polynomials and integration operation matrix for approximating of function and its derivatives. We convert the original problem for finding the eigenvalues of Sturm-Liouville problem to a problem of ...

We present the extension of the successful Constant Perturbation Method (CPM) for Schrödinger problems to the more general class of Sturm-Liouville eigenvalue problems. Whereas the orginal CPM can only be applied to Sturm-Liouville problems after a Liouville transformation, the more general CPM presented here solves the Sturm-Liouville problem directly. This enlarges the range of applicability ...

This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov’s method as well as boundary value methods for second order regular Sturm-L...