A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane

A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function U (a, z) in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly efficient method based on a fourth-order fixed point method with...

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Autores: Dunster, T.M., Gil Gómez, Amparo|||0000-0002-7449-4205, Ruiz Antolín, Diego|||0000-0001-8011-6529, Segura Sala, José Javier|||0000-0002-0841-5636
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/36372
Acceso en línea:https://hdl.handle.net/10902/36372
Access Level:acceso abierto
Palabra clave:Parabolic cylinder functions
Complex zeros
Fixed point methods
Matlab software
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spelling A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex planeDunster, T.M.Gil Gómez, Amparo|||0000-0002-7449-4205Ruiz Antolín, Diego|||0000-0001-8011-6529Segura Sala, José Javier|||0000-0002-0841-5636Parabolic cylinder functionsComplex zerosFixed point methodsMatlab softwareA numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function U (a, z) in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly efficient method based on a fourth-order fixed point method with the parabolic cylinder functions computed by Taylor series and carefully selected steps, to compute the rest of the zeros. For |a| small, the asymptotic approximations are complemented with a few fixed point iterations requiring the evaluation of U (a, z) and U' (a,z) in the region where the complex zeros are located. Liouville Green expansions are derived to enhance the performance of a computational scheme to evaluate U (a, z) and U' (a,z) in that region. Several tests show the accuracy and efficiency of the numerical algorithm.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Financial support was received from Ministerio de Economía y Competitividad, Project PID2021-127252NB-I00 (MCIN/AEI/10.13039/501100011033/ FEDER, UE.Springer NatureUniversidad de Cantabria20252025-06-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/36372BIT numerical mathematics, 2025, 65(2), 20reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/363722026-06-02T12:39:31Z
dc.title.none.fl_str_mv A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
title A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
spellingShingle A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
Dunster, T.M.
Parabolic cylinder functions
Complex zeros
Fixed point methods
Matlab software
title_short A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
title_full A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
title_fullStr A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
title_full_unstemmed A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
title_sort A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
dc.creator.none.fl_str_mv Dunster, T.M.
Gil Gómez, Amparo|||0000-0002-7449-4205
Ruiz Antolín, Diego|||0000-0001-8011-6529
Segura Sala, José Javier|||0000-0002-0841-5636
author Dunster, T.M.
author_facet Dunster, T.M.
Gil Gómez, Amparo|||0000-0002-7449-4205
Ruiz Antolín, Diego|||0000-0001-8011-6529
Segura Sala, José Javier|||0000-0002-0841-5636
author_role author
author2 Gil Gómez, Amparo|||0000-0002-7449-4205
Ruiz Antolín, Diego|||0000-0001-8011-6529
Segura Sala, José Javier|||0000-0002-0841-5636
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Parabolic cylinder functions
Complex zeros
Fixed point methods
Matlab software
topic Parabolic cylinder functions
Complex zeros
Fixed point methods
Matlab software
description A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function U (a, z) in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly efficient method based on a fourth-order fixed point method with the parabolic cylinder functions computed by Taylor series and carefully selected steps, to compute the rest of the zeros. For |a| small, the asymptotic approximations are complemented with a few fixed point iterations requiring the evaluation of U (a, z) and U' (a,z) in the region where the complex zeros are located. Liouville Green expansions are derived to enhance the performance of a computational scheme to evaluate U (a, z) and U' (a,z) in that region. Several tests show the accuracy and efficiency of the numerical algorithm.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-06-01
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/10902/36372
url https://hdl.handle.net/10902/36372
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 4.0 International
http://creativecommons.org/licenses/by/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 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv BIT numerical mathematics, 2025, 65(2), 20
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 15.811543

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