This paper deals with the numerical solution of a λ-rational Sturm-Liouville problem using the shooting technique. Some classical procedures (boundary value methods and shooting with the Magnus method) are applied in order to examine their effectiveness in the presence of an eigenvalue embedded in the essential spectrum. It is shown that all these methods experience a degeneration of their order of accuracy: none, regardless of the order it may have on a classical Sturm-Liouville problem, has order greater than 2. Moreover, this situation cannot be rectified by applying the regularizing transformation of Niessen and Zettl. Nevertheless, it is possible to generalize a very efficient correction technique, first suggested by the authors for classical Sturm-Liouville problems, to the present case.
Numerical solution of a lambda-rational Sturm-Liouville problem
GHELARDONI, PAOLO;GHERI, GIOVANNI;
2003-01-01
Abstract
This paper deals with the numerical solution of a λ-rational Sturm-Liouville problem using the shooting technique. Some classical procedures (boundary value methods and shooting with the Magnus method) are applied in order to examine their effectiveness in the presence of an eigenvalue embedded in the essential spectrum. It is shown that all these methods experience a degeneration of their order of accuracy: none, regardless of the order it may have on a classical Sturm-Liouville problem, has order greater than 2. Moreover, this situation cannot be rectified by applying the regularizing transformation of Niessen and Zettl. Nevertheless, it is possible to generalize a very efficient correction technique, first suggested by the authors for classical Sturm-Liouville problems, to the present case.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
