On the calculation of the finite Hankel transform eigenfunctions

In this work, we discuss the numerical computation of the eigenvalues and eigenfunctions of the finite (truncated) Hankel transform, important for numerous applications. Due to the very special behavior of the Hankel transform eigenfunctions, their direct numerical calculation often causes an essent...

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Vydané v:Journal of applied mathematics & computing Ročník 43; číslo 1-2; s. 151 - 173
Hlavní autori: Amodio, P., Levitina, T., Settanni, G., Weinmüller, E. B.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2013
Springer Nature B.V
Predmet:
Accuracy
Applied mathematics
Approximation
Boundary conditions
Computation
Computational mathematics
Computational Mathematics and Numerical Analysis
Computer science
Eigenfunctions
Eigenvalues
Fourier transforms
Mathematical analysis
Mathematical and Computational Engineering
Mathematical models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical analysis
Operators
Ordinary differential equations
Original Research
Studies
Theory of Computation
Transforms
Finite Hankel transform
65R10
Prüfer angle
34B16
65L15
65R20
34B24
Singular Sturm-Liouville problem
Finite difference schemes
34L16
65F15
Generalized spheroidal wave functions
65L10
ISSN:1598-5865, 1865-2085
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Popis
Shrnutí:In this work, we discuss the numerical computation of the eigenvalues and eigenfunctions of the finite (truncated) Hankel transform, important for numerous applications. Due to the very special behavior of the Hankel transform eigenfunctions, their direct numerical calculation often causes an essential loss of accuracy. Here, we present several simple, efficient and robust numerical techniques to compute Hankel transform eigenfunctions via the associated singular self-adjoint Sturm-Liouville operator. The properties of the proposed approaches are compared and illustrated by means of numerical experiments.
Bibliografia:SourceType-Scholarly Journals-1
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-013-0657-1