Two-parameter Sturm-Liouville problems

TL;DR

This paper demonstrates the application of the Regularized Sampling Method to compute eigenvalues of two-parameter Sturm-Liouville problems, extending its effectiveness to more complex cases with an illustrative example.

Contribution

It introduces the use of the Regularized Sampling Method for two-parameter Sturm-Liouville problems, a novel extension of its previous applications.

Findings

The method successfully computes eigenvalues for two-parameter SL problems.

The approach is effective for complex SL problems including singular and non-self-adjoint cases.

An example confirms the method's practical applicability.

Abstract

This paper deals with the computation of the eigenvalues of two-parameter Sturm- Liouville (SL) problems using the Regularized Sampling Method, a method which has been effective in computing the eigenvalues of broad classes of SL problems (Singular, Non-Self-Adjoint, Non-Local, Impulsive,...). We have shown, in this work that it can tackle two-parameter SL problems with equal ease. An example was provided to illustrate the effectiveness of the method.