Numerical solution of the inverse spectral problem for Bessel operators

We consider some inverse spectral problems associated with the singular Sturm–Liouville equation − u ″ + ( q ( x ) + ℓ ( ℓ + 1 ) x 2 ) u = λ u 0 < x < 1 for ℓ = 1 , 2 … , which is obtained by separation of variables in the 3D radial Schrödinger equation. One approach to such problems involves...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 235; no. 1; pp. 120 - 136
Main Authors: Hryniv, Rostyslav, Sacks, Paul
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.11.2010
Elsevier
Subjects:
Bessel equation
Computation
Computational method
Exact sciences and technology
Global analysis, analysis on manifolds
Inverse
Inverse spectral problem
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Operators
Ordinary differential equations
Partial differential equations
Schroedinger equation
Sciences and techniques of general use
Spectra
Sturm–Liouville equation
Three dimensional
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Transformations
Bessel equation
Computational method
Inverse spectral problem
Sturm–Liouville equation
Spectral operator
Numerical analysis
Three-dimensional calculations
Applied mathematics
Numerical solution
Singular equation
Sturm-Liouville equation
Schrödinger equation
Inverse problem
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:We consider some inverse spectral problems associated with the singular Sturm–Liouville equation − u ″ + ( q ( x ) + ℓ ( ℓ + 1 ) x 2 ) u = λ u 0 < x < 1 for ℓ = 1 , 2 … , which is obtained by separation of variables in the 3D radial Schrödinger equation. One approach to such problems involves the use of almost isospectral transformations, by means of which a reduction to a similar problem in the classical ℓ = 0 case is possible. In this paper we focus on the development of computational techniques suggested by these ideas.
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2010.05.018