Computation of parabolic cylinder functions having complex argument

Numerical methods for the computation of the parabolic cylinder function U(a,z) for real a and complex z are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stab...

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Detalles Bibliográficos
Autores: Dunster, T.M., Gil Gómez, Amparo|||0000-0002-7449-4205, Segura Sala, José Javier|||0000-0002-0841-5636
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/31000
Acceso en línea:https://hdl.handle.net/10902/31000
Access Level:acceso abierto
Palabra clave:Parabolic cylinder functions
Asymptotic expansions
Numerical quadrature
Numerical algorithms
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spelling Computation of parabolic cylinder functions having complex argumentDunster, T.M.Gil Gómez, Amparo|||0000-0002-7449-4205Segura Sala, José Javier|||0000-0002-0841-5636Parabolic cylinder functionsAsymptotic expansionsNumerical quadratureNumerical algorithmsNumerical methods for the computation of the parabolic cylinder function U(a,z) for real a and complex z are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stable integral representations; these two main methods can be complemented with Maclaurin series and a Poincaré asymptotic expansion. We provide numerical evidence showing that the combination of these methods is enough for computing the function with 5 × 10-13 relative accuracy in double precision floating point arithmetic.The authors acknowledge financial support from Ministerio de Ciencia e Innovación, projects PGC2018-098279-B-I00 (MCIN/AEI/10.13039/ 501100011033/FEDER “Una manera de hacer Europa”) and PID2021-127252NB-I00 (MCIN/AEI/10.13039/ 501100011033/FEDER, UE).ElsevierUniversidad de Cantabria20242024-03-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/31000Applied Numerical Mathematics, 2024, 197, 230-242reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/310002026-06-02T12:39:31Z
dc.title.none.fl_str_mv Computation of parabolic cylinder functions having complex argument
title Computation of parabolic cylinder functions having complex argument
spellingShingle Computation of parabolic cylinder functions having complex argument
Dunster, T.M.
Parabolic cylinder functions
Asymptotic expansions
Numerical quadrature
Numerical algorithms
title_short Computation of parabolic cylinder functions having complex argument
title_full Computation of parabolic cylinder functions having complex argument
title_fullStr Computation of parabolic cylinder functions having complex argument
title_full_unstemmed Computation of parabolic cylinder functions having complex argument
title_sort Computation of parabolic cylinder functions having complex argument
dc.creator.none.fl_str_mv Dunster, T.M.
Gil Gómez, Amparo|||0000-0002-7449-4205
Segura Sala, José Javier|||0000-0002-0841-5636
author Dunster, T.M.
author_facet Dunster, T.M.
Gil Gómez, Amparo|||0000-0002-7449-4205
Segura Sala, José Javier|||0000-0002-0841-5636
author_role author
author2 Gil Gómez, Amparo|||0000-0002-7449-4205
Segura Sala, José Javier|||0000-0002-0841-5636
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Parabolic cylinder functions
Asymptotic expansions
Numerical quadrature
Numerical algorithms
topic Parabolic cylinder functions
Asymptotic expansions
Numerical quadrature
Numerical algorithms
description Numerical methods for the computation of the parabolic cylinder function U(a,z) for real a and complex z are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stable integral representations; these two main methods can be complemented with Maclaurin series and a Poincaré asymptotic expansion. We provide numerical evidence showing that the combination of these methods is enough for computing the function with 5 × 10-13 relative accuracy in double precision floating point arithmetic.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-03-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/31000
url https://hdl.handle.net/10902/31000
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv Applied Numerical Mathematics, 2024, 197, 230-242
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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