MATLAB GUI for computing Bessel functions using continued fractions algorithm

[EN] Higher order Bessel functions are prevalent in physics and engineering and there exist different methods to evaluate them quickly and efficiently. Two of these methods are Miller's algorithm and the continued fractions algorithm. Miller's algorithm uses arbitrary starting valu...

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Detalles Bibliográficos
Autores: Hernandez Vargas, E., Commeford, K., Pérez Quiles, María Jezabel
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/138035
Acceso en línea:https://riunet.upv.es/handle/10251/138035
Access Level:acceso abierto
Palabra clave:Funções de Bessel
Frações continuadas
GUI em Matlab
Bessel functions, continued fraction, Matlab GUI
MATEMATICA APLICADA
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spelling MATLAB GUI for computing Bessel functions using continued fractions algorithmGUI Matlab para o cálculo de funções de Bessel usando frações continuadasHernandez Vargas, E.Commeford, K.Pérez Quiles, María JezabelFunções de BesselFrações continuadasGUI em MatlabBessel functions, continued fraction, Matlab GUIMATEMATICA APLICADA[EN] Higher order Bessel functions are prevalent in physics and engineering and there exist different methods to evaluate them quickly and efficiently. Two of these methods are Miller's algorithm and the continued fractions algorithm. Miller's algorithm uses arbitrary starting values and normalization constants to evaluate Bessel functions. The continued fractions algorithm directly computes each value, keeping the error as small as possible. Both methods respect the stability of the Bessel function recurrence relations. Here we outline both methods and explain why the continued fractions algorithm is more efficient. The goal of this paper is both (1) to introduce the continued fractions algorithm to physics and engineering students and (2) to present a MATLAB GUI (Graphic User Interface) where this method has been used for computing the Semi-integer Bessel Functions and their zeros.[PT] Funções de Bessel de ordem mais alta são recorrentes em física e nas engenharias, sendo que há diferentes métodos para calculá-las de maneira rápida e eficiente. Dois destes métodos são o algoritmo de Miller e o algoritmo de frações continuadas. O primeiro faz uso de valores iniciais e constantes de normalização arbitrários, enquanto o segundo o faz calculando cada valor diretamente, minimizando tanto quanto possível o erro. Ambos respeitam a estabilidade das relações de recorrência das funções de Bessel. Neste trabalho descrevemos ambos os métodos e explicamos a razão pela qual o algoritmo das frações continuadas é mais eficiente. O objetivo do artigo é (1) introduzir o algoritmo de frações continuadas para estudantes de física e das engenharias e (2) apresentar um GUI (Graphic User Interface) em Matlab no qual este método foi utilizado para calcular funções de Bessel semi-inteiras e seus zeros.The authors wish to thank the financial support received from the Universidad Politécnica de Valencia under grant PAID-06-09-2734, from the Ministerio de Ciencia e Innovación through grant ENE2008-00599 and specially from the Generalitat Valenciana under grant reference 3012/2009.SciELODepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería IndustrialUniversitat Politècnica de ValènciaMinisterio de Ciencia e InnovaciónGeneralitat ValencianaRepositorio Institucional de la Universitat Politècnica de València Riunet20112011-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/138035reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengUniversitat Politècnica de València https://doi.org/10.13039/501100004233 PAID-06-09-2734Generalitat Valenciana https://doi.org/10.13039/501100003359 GV%2F3012%2F2009Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 ENE2008-00599 MODELADO, SIMULACION Y VALIDACION EXPERIMENTAL DE LA TRANSFERENCIA DE CALOR EN EL ENTORNO DE LA EDIFICACIONopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial (by-nc) http://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1380352026-06-13T07:49:27Z
dc.title.none.fl_str_mv MATLAB GUI for computing Bessel functions using continued fractions algorithm
GUI Matlab para o cálculo de funções de Bessel usando frações continuadas
title MATLAB GUI for computing Bessel functions using continued fractions algorithm
spellingShingle MATLAB GUI for computing Bessel functions using continued fractions algorithm
Hernandez Vargas, E.
Funções de Bessel
Frações continuadas
GUI em Matlab
Bessel functions, continued fraction, Matlab GUI
MATEMATICA APLICADA
title_short MATLAB GUI for computing Bessel functions using continued fractions algorithm
title_full MATLAB GUI for computing Bessel functions using continued fractions algorithm
title_fullStr MATLAB GUI for computing Bessel functions using continued fractions algorithm
title_full_unstemmed MATLAB GUI for computing Bessel functions using continued fractions algorithm
title_sort MATLAB GUI for computing Bessel functions using continued fractions algorithm
dc.creator.none.fl_str_mv Hernandez Vargas, E.
Commeford, K.
Pérez Quiles, María Jezabel
author Hernandez Vargas, E.
author_facet Hernandez Vargas, E.
Commeford, K.
Pérez Quiles, María Jezabel
author_role author
author2 Commeford, K.
Pérez Quiles, María Jezabel
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Industrial
Universitat Politècnica de València
Ministerio de Ciencia e Innovación
Generalitat Valenciana
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Funções de Bessel
Frações continuadas
GUI em Matlab
Bessel functions, continued fraction, Matlab GUI
MATEMATICA APLICADA
topic Funções de Bessel
Frações continuadas
GUI em Matlab
Bessel functions, continued fraction, Matlab GUI
MATEMATICA APLICADA
description [EN] Higher order Bessel functions are prevalent in physics and engineering and there exist different methods to evaluate them quickly and efficiently. Two of these methods are Miller's algorithm and the continued fractions algorithm. Miller's algorithm uses arbitrary starting values and normalization constants to evaluate Bessel functions. The continued fractions algorithm directly computes each value, keeping the error as small as possible. Both methods respect the stability of the Bessel function recurrence relations. Here we outline both methods and explain why the continued fractions algorithm is more efficient. The goal of this paper is both (1) to introduce the continued fractions algorithm to physics and engineering students and (2) to present a MATLAB GUI (Graphic User Interface) where this method has been used for computing the Semi-integer Bessel Functions and their zeros.
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/138035
url https://riunet.upv.es/handle/10251/138035
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Universitat Politècnica de València https://doi.org/10.13039/501100004233 PAID-06-09-2734
Generalitat Valenciana https://doi.org/10.13039/501100003359 GV%2F3012%2F2009
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 ENE2008-00599 MODELADO, SIMULACION Y VALIDACION EXPERIMENTAL DE LA TRANSFERENCIA DE CALOR EN EL ENTORNO DE LA EDIFICACION
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial (by-nc)
http://creativecommons.org/licenses/by-nc/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
Reconocimiento - No comercial (by-nc)
http://creativecommons.org/licenses/by-nc/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv SciELO
publisher.none.fl_str_mv SciELO
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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