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Using the SLEDGE package on Sturm-Liouville problems having nonempty essential spectra

Editor: Ronald Boisvert Authors:

Michael S. P. Eastham,

Charles T. Fulton,

Steven PruessAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 22, Issue 4

Pages 423 - 446

https://doi.org/10.1145/235815.235819

Published: 01 December 1996 Publication History

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Abstract

We describe the performance of the Sturm-Liouville software package SLEDGE on a variety of problems having continuous spectra. The code's output is shown to be in good accord with a wide range of known theoretical results.

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Cited By

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Baeyens TVan Daele M(2020)The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equationsComputer Physics Communications10.1016/j.cpc.2020.107568(107568)Online publication date: Aug-2020
https://doi.org/10.1016/j.cpc.2020.107568
ZHANG YHUANG ZZHANG X(2010)Computing Eigenvalues of Left-Definite Sturm-Liouville ProblemsActa Analysis Functionalis Applicata10.3724/SP.J.1160.2010.0011012:2(110-114)Online publication date: 19-Sep-2010
https://doi.org/10.3724/SP.J.1160.2010.00110
Eastham M(2010)On the location of spectral concentration for Sturm–Liouville problems with rapidly decaying potentialMathematika10.1112/S002557930001401745:01(25)Online publication date: 26-Feb-2010
https://doi.org/10.1112/S0025579300014017
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Index Terms

Using the SLEDGE package on Sturm-Liouville problems having nonempty essential spectra
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
  2. Mathematical software

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The software package SLEDGE has as one of its options the estimation of spectral density functions p(t) for a wide class of singular Strurm-Liouville problems. In this article the underlaying theory and implementation issues are discussed. Several ...
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Software is described for the Sturm-Liouville eigenproblem. Eigenvalues, eigenfunctions, and spectral density functions can be estimated with global error control. The method of approximating the coefficients forms the mathematical basis. The underlying ...
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We identify a class of Sturm-Liouville equations with transmission conditions such that any Sturm-Liouville problem consisting of such an equation with transmission condition and an arbitrary separated or real coupled self-adjoint boundary condition has ...

Reviews

Reviewer: Lawrence Shampine

SLEDGE is an excellent package for the numerical solution of both regular and singular Sturm-Liouville problems. At present, it is the only package that attempts to estimate the spectral density function for a singular problem with continuous spectrum. This paper describes the solutions of a variety of examples for which there are theoretical results that can be used to study how well the package is able to simulate a singular spectral density function. The performance of the package is most impressive.

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Information

Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 22, Issue 4

Dec. 1996

116 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/235815

Editor:
Ronald Boisvert
National Institute of Standards and Technology, Guithersburg, MD

Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 1996

Published in TOMS Volume 22, Issue 4

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Baeyens TVan Daele M(2020)The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equationsComputer Physics Communications10.1016/j.cpc.2020.107568(107568)Online publication date: Aug-2020
https://doi.org/10.1016/j.cpc.2020.107568
ZHANG YHUANG ZZHANG X(2010)Computing Eigenvalues of Left-Definite Sturm-Liouville ProblemsActa Analysis Functionalis Applicata10.3724/SP.J.1160.2010.0011012:2(110-114)Online publication date: 19-Sep-2010
https://doi.org/10.3724/SP.J.1160.2010.00110
Eastham M(2010)On the location of spectral concentration for Sturm–Liouville problems with rapidly decaying potentialMathematika10.1112/S002557930001401745:01(25)Online publication date: 26-Feb-2010
https://doi.org/10.1112/S0025579300014017
Fulton CPearson DPruess S(2005)Computing the spectral function for singular Sturm-Liouville problemsJournal of Computational and Applied Mathematics10.5555/1056329.1716603176:1(131-162)Online publication date: 1-Apr-2005
https://dl.acm.org/doi/10.5555/1056329.1716603
Fulton CPearson DPruess S(2005)Computing the spectral function for singular Sturm–Liouville problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2004.07.006176:1(131-162)Online publication date: Apr-2005
https://doi.org/10.1016/j.cam.2004.07.006
Brown BEvans W(2002)Prof. Michael Eastham LaudatumJournal of Computational and Applied Mathematics10.5555/638714.638716148:1(.11-.13)Online publication date: 1-Nov-2002
https://dl.acm.org/doi/10.5555/638714.638716
Brown BEvans W(2002)Prof. Michael Eastham LaudatumJournal of Computational and Applied Mathematics10.1016/S0377-0427(02)00756-2148:1(xi-xiii)Online publication date: Nov-2002
https://doi.org/10.1016/S0377-0427(02)00756-2
Brown BEastham MMcCormack D(1998)Absolute continuity and spectral concentration for slowly decaying potentialsJournal of Computational and Applied Mathematics10.1016/S0377-0427(98)00087-994:2(181-197)Online publication date: 3-Aug-1998
https://dl.acm.org/doi/10.1016/S0377-0427%2898%2900087-9
Brown BEastham MMcCormack D(1997)Spectral concentration and rapidly decaying potentialsJournal of Computational and Applied Mathematics10.1016/S0377-0427(97)00072-181:2(333-348)Online publication date: 8-Jul-1997
https://dl.acm.org/doi/10.1016/S0377-0427%2897%2900072-1

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Abstract

References

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Index Terms

Recommendations

The computation of spectral density functions for singular Sturm-Liouville problems involving simple continuous spectra

Mathematical software for Sturm-Liouville problems

Matrix representations of Sturm-Liouville problems with transmission conditions

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