This paper presents a method of numerically computing zeros of an analytic function for the specific application of computing eigenvalues of the Sturm-Liouville problem. The Sturm-Liouville problem is an infinite dimensional eigenvalue problem that often arises in solving partial differential equations, including the heat and wave equations. To compute eigenvalues of the Sturm-Liouville problem...

We give a comprehensive treatment of Sturm–Liouville operators whose coefficients are measures including a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl–Titchmarsh–Kodaira theory. We avoid previous technical restrictions and, at the same time, extend all results to a larger class of operators. Our operators include classical Sturm– Liouville operators,...

We prove a necessary optimality condition for isoperimetric problems on time scales in the space of delta-differentiable functions with rdcontinuous derivatives. The results are then applied to Sturm-Liouville eigenvalue problems on time scales.

An algorithm is presented for computing eigenvalues of regular selfadjoint Sturm-Liouville (SL) problems with matrix coefficients and separated boundary conditions.

In this lecture we abstract the eigenvalue problems that we have found so useful thus far for solving the PDEs to a general class of boundary value problems that share a common set of properties. The so-called Sturm-Liouville Problems define a class of eigenvalue problems, which include many of the previous problems as special cases. The S − L Problem helps to identify those assumptions that ar...

the purpose of this article is to use the classical sampling theorem, wks sampling theorem, to deriveapproximate values of the eigenvalues of the sturm-liouville problems with eigenparameter in the boundaryconditions. error analysis is used to give estimates of the associated error. higher order approximations are also drived, which lead to more complicated computations. we give some examples a...

‎In this manuscript‎, ‎we study various by uniqueness results for inverse spectral problems of Sturm--Liouville operators using three spectrum with a finite number of discontinuities at interior points which we impose the usual transmission conditions‎. ‎We consider both the cases of classical Robin and eigenparameter dependent boundary conditions.