Eigenvalues of Vectorial Sturm-Liouville Problems with Parameter Dependent Boundary Conditions

Abstract

We generalize the regularized sampling method introduced in 2005 by the author to compute the eigenvalues of scalar Sturm-Liouville problems (SLPs) to the case of vectorial SLP with parameter dependent boundary conditions. A few problems are worked out to illustrate the effectiveness of the method and show by the same token that we have indeed a general method capable of handling with ease very broad classes of SLPs, whether scalar or vectorial.