On some numerical methods for spectral computations in lambda-rational Sturm-Liouville problems

This paper is concerned with the numerical solution of a λ-rational Sturm-Liouville problem. Classical methods are considered in connection with the shooting technique used via the method of Magnus series and boundary value methods. We prove that, in the presence of an eigenvalue embedded in the essential spectrum, these methods exhibit a decay in their performance. Nevertheless some boundary value methods used in a non-standard form behave as in the standard form in regular problems preserving a high order of convergence. Numerical experiments confirm the theory.