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The SLEIGN2 code is based on the ideas and methods of the original SLEIGN code of 1979. The main purpose of the SLEIGN2 code is to compute eigenvalues and eigenfunctions of regular and singular self-adjoint Sturm-Liouville problems, with both separated and coupled boundary conditions, and to approximate the continuous spectrum in the singular case. The code(More)
Given any self-adjoint realization S of a singular Sturm-Liouville (S-L) problem, it is possible to construct a sequence {Sr} of regular S-L problems with the properties (i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of {Sr} (ii) in the case when S is regular or limit-circle at each(More)
The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on boundary points. The derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. This for arbitrary (separated or coupled) self-adjoint regular boundary conditions. In addition, as the length of the interval shrinks(More)
We consider some geometric aspects of regular Sturm-Liouville problems. First, we clarify a natural geometric structure on the space of boundary conditions. This structure is the base for studying the dependence of Sturm-Liouville eigenvalues on the boundary condition, and reveals many new properties of these eigenvalues. In particular, the eigenvalues for(More)
SLEIGN is a software package for the computation of eigenvalues and eigenfunction:s of regular and singular Sturm Liouville boundary value problems, The package is a modification and extension of a code with the same name developed by Bailey, Gordon, and Shampinej which is described in ACM Z’OMS 4 (1978), 193-208. The modifications and extensions include(More)
The package comprises two user-visible subprograms, sleign and zcount, and a set of special purpose subprograms invoked from them; the integration of the differential equations is done by the GERK software of Shampine and Watts [31 included with the package. zcount is used in the initial step for the semidefinite problem [1] to determine the translated(More)
The generalized Sturm-Liouville problems in this paper stem from the ideas of Christ Shubin and Stolz, based on introducing singularities at a countable number of regular points on the real line. This idea is generalized to the introduction of a countable number of regular or limitcircle singular points. These results are shown to link with the work of(More)
which lies below the essential spectrum. In this paper we extend and develop further the notions in [3] to cover additional classes of problems. In Section 2 we introduce the relevant notation and review the approach taken in [3]. In Section 3 we show how some of the restrictions required by the approach in [3] may be removed enabling us to prove the(More)