In this paper, we describe how to approximate numerically the eigenvalues of a Sturm-Liouville problem defined on a semi-infinite interval. The key idea is to transform the problem in such a way as to compress the semi-infinite interval in a finite interval by applying a suitable change of the independent variable. Then, we approximate each derivative in the Sturm-Liouville equation thus obtained with finite difference schemes. Consequently, we convert the Sturm-Liouville problem into an algebraic eigenvalue problem. The numerical results of the experiments show that the proposed approach is promising.

Approximation of eigenvalues of Sturm-Liouville problems defined on a semi-infinite domain

Lidia Aceto
2020

Abstract

In this paper, we describe how to approximate numerically the eigenvalues of a Sturm-Liouville problem defined on a semi-infinite interval. The key idea is to transform the problem in such a way as to compress the semi-infinite interval in a finite interval by applying a suitable change of the independent variable. Then, we approximate each derivative in the Sturm-Liouville equation thus obtained with finite difference schemes. Consequently, we convert the Sturm-Liouville problem into an algebraic eigenvalue problem. The numerical results of the experiments show that the proposed approach is promising.
Mebirouk, Abdelmouemin; Bouheroum-Mentri, Sabria; Aceto, Lidia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1009650
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