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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Vydané v:	Journal of computational and applied mathematics Ročník 235; číslo 1; s. 120 - 136
Hlavní autori:	Hryniv, Rostyslav, Sacks, Paul
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Kidlington Elsevier B.V 01.11.2010 Elsevier
Predmet:	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
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Popis
Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2010.05.018