We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α ∈ (3/2, 2) on the unit interval (0, 1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα−1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value pro...

We classify the general linear boundary conditions involving u′′, u′ and u on the boundary {a, b} so that a Sturm-Liouville operator on [a, b] has a unique self-adjoint extension on a suitable Hilbert space.

We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally has the same spectral properties as a definitizable operator.

We propose a numerical algorithm for solving inverse problems of spectral analysis for Sturm–Liouville differential operators on the half-line. Moreover some results of numerical experiments are also presented. AMS subject classification: 65L09, 34A55, 47E05.

— In this work, we use the regularized sampling method to compute the eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval. We work out an example by computing a few eigenvalues and their corresponding eigenfunctions.

This article presents an overview of the recent literature and summarises the major theoretical developments pertaining to a class of non-Sturm-Liouville orthogonality relations relevant to fluid-structure interaction.

We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator ?4 d 2 ds 2 + 2 (s) with potential given by the curvature of a closed curve.

In this study we investigate asymptotic behavior of eigenvalues and eigenfunctions of one discontinuous Sturm-Liouville problem with eigendependent boundary and transmission conditions. c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.