Approximation of the modified error function

Autores
Ceretani, Andrea Noemí; Salva, Natalia Nieves; Tarzia, Domingo Alberto
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión aceptada
Descripción
In this article, we obtain explicit approximations of the modified error function introduced in Cho and Sunderland (1974), as part of a Stefan problem with a temperature-dependent thermal conductivity. This function depends on a parameter δ, which is related to the ther- mal conductivity in the original phase-change process. We propose a method to obtain ap- proximations, which is based on the assumption that the modified error function admits a power series representation in δ. Accurate approximations are obtained through functions involving error and exponential functions only. For the special case in which δassumes small positive values, we show that the modified error function presents some character- istic features of the classical error function, such as monotony, concavity, and boundedness. Moreover, we prove that the modified error function converges to the classical one when δgoes to zero.
Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Ceretani, Andrea Noemí. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemática; Argentina.
Fil: Salva, Natalia Nieves. Universidad Nacional del Comahue. Centro Regional Universitario Bariloche. Departamento de Matemática; Argentina.
Fil: Salva, Natalia Nieves. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche. Departamento de Mecánica Computacional; Argentina.
Fil: Salva, Natalia Nieves. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemática; Argentina
Fuente
Applied Mathematics and Computation. Vol. 337 (2018)
Materia
Modified error function
Error function
Phase change problem
Temperature dependent thermal
Conductivity
Nonlinear second order ordinary differential equation
Ciencias Aplicadas
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
Repositorio Digital Institucional (UNCo)
Institución
Universidad Nacional del Comahue
OAI Identificador
oai:rdi.uncoma.edu.ar:uncomaid/17308
Acceder
id RDIUNCO_ccf997974f01a86ae8d88c5fe907a482
oai_identifier_str oai:rdi.uncoma.edu.ar:uncomaid/17308
network_acronym_str RDIUNCO
repository_id_str 7108
network_name_str Repositorio Digital Institucional (UNCo)
spelling Approximation of the modified error functionCeretani, Andrea NoemíSalva, Natalia NievesTarzia, Domingo AlbertoModified error functionError functionPhase change problemTemperature dependent thermalConductivityNonlinear second order ordinary differential equationCiencias AplicadasIn this article, we obtain explicit approximations of the modified error function introduced in Cho and Sunderland (1974), as part of a Stefan problem with a temperature-dependent thermal conductivity. This function depends on a parameter δ, which is related to the ther- mal conductivity in the original phase-change process. We propose a method to obtain ap- proximations, which is based on the assumption that the modified error function admits a power series representation in δ. Accurate approximations are obtained through functions involving error and exponential functions only. For the special case in which δassumes small positive values, we show that the modified error function presents some character- istic features of the classical error function, such as monotony, concavity, and boundedness. Moreover, we prove that the modified error function converges to the classical one when δgoes to zero.Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Ceretani, Andrea Noemí. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemática; Argentina.Fil: Salva, Natalia Nieves. Universidad Nacional del Comahue. Centro Regional Universitario Bariloche. Departamento de Matemática; Argentina.Fil: Salva, Natalia Nieves. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche. Departamento de Mecánica Computacional; Argentina.Fil: Salva, Natalia Nieves. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemática; ArgentinaElsevier2018-11-15info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfpp. 607-617application/pdf0096-3003http://rdi.uncoma.edu.ar/handle/uncomaid/17308Applied Mathematics and Computation. Vol. 337 (2018)reponame:Repositorio Digital Institucional (UNCo)instname:Universidad Nacional del Comahueenghttps://doi.org/10.1016/j.amc.2018.05.054info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/2026-08-26T10:58:30Zoai:rdi.uncoma.edu.ar:uncomaid/17308instacron:UNCoInstitucionalhttp://rdi.uncoma.edu.ar/Universidad públicaNo correspondehttp://rdi.uncoma.edu.ar/oaimirtha.mateo@biblioteca.uncoma.edu.ar; adriana.acuna@biblioteca.uncoma.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:71082026-08-26 10:58:30.333Repositorio Digital Institucional (UNCo) - Universidad Nacional del Comahuefalse
dc.title.none.fl_str_mv Approximation of the modified error function
title Approximation of the modified error function
spellingShingle Approximation of the modified error function
Ceretani, Andrea Noemí
Modified error function
Error function
Phase change problem
Temperature dependent thermal
Conductivity
Nonlinear second order ordinary differential equation
Ciencias Aplicadas
title_short Approximation of the modified error function
title_full Approximation of the modified error function
title_fullStr Approximation of the modified error function
title_full_unstemmed Approximation of the modified error function
title_sort Approximation of the modified error function
dc.creator.none.fl_str_mv Ceretani, Andrea Noemí
Salva, Natalia Nieves
Tarzia, Domingo Alberto
author Ceretani, Andrea Noemí
author_facet Ceretani, Andrea Noemí
Salva, Natalia Nieves
Tarzia, Domingo Alberto
author_role author
author2 Salva, Natalia Nieves
Tarzia, Domingo Alberto
author2_role author
author
dc.subject.none.fl_str_mv Modified error function
Error function
Phase change problem
Temperature dependent thermal
Conductivity
Nonlinear second order ordinary differential equation
Ciencias Aplicadas
topic Modified error function
Error function
Phase change problem
Temperature dependent thermal
Conductivity
Nonlinear second order ordinary differential equation
Ciencias Aplicadas
dc.description.none.fl_txt_mv In this article, we obtain explicit approximations of the modified error function introduced in Cho and Sunderland (1974), as part of a Stefan problem with a temperature-dependent thermal conductivity. This function depends on a parameter δ, which is related to the ther- mal conductivity in the original phase-change process. We propose a method to obtain ap- proximations, which is based on the assumption that the modified error function admits a power series representation in δ. Accurate approximations are obtained through functions involving error and exponential functions only. For the special case in which δassumes small positive values, we show that the modified error function presents some character- istic features of the classical error function, such as monotony, concavity, and boundedness. Moreover, we prove that the modified error function converges to the classical one when δgoes to zero.
Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Ceretani, Andrea Noemí. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemática; Argentina.
Fil: Salva, Natalia Nieves. Universidad Nacional del Comahue. Centro Regional Universitario Bariloche. Departamento de Matemática; Argentina.
Fil: Salva, Natalia Nieves. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche. Departamento de Mecánica Computacional; Argentina.
Fil: Salva, Natalia Nieves. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemática; Argentina
description In this article, we obtain explicit approximations of the modified error function introduced in Cho and Sunderland (1974), as part of a Stefan problem with a temperature-dependent thermal conductivity. This function depends on a parameter δ, which is related to the ther- mal conductivity in the original phase-change process. We propose a method to obtain ap- proximations, which is based on the assumption that the modified error function admits a power series representation in δ. Accurate approximations are obtained through functions involving error and exponential functions only. For the special case in which δassumes small positive values, we show that the modified error function presents some character- istic features of the classical error function, such as monotony, concavity, and boundedness. Moreover, we prove that the modified error function converges to the classical one when δgoes to zero.
publishDate 2018
dc.date.none.fl_str_mv 2018-11-15
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv 0096-3003
http://rdi.uncoma.edu.ar/handle/uncomaid/17308
identifier_str_mv 0096-3003
url http://rdi.uncoma.edu.ar/handle/uncomaid/17308
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://doi.org/10.1016/j.amc.2018.05.054
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
pp. 607-617
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv Applied Mathematics and Computation. Vol. 337 (2018)
reponame:Repositorio Digital Institucional (UNCo)
instname:Universidad Nacional del Comahue
reponame_str Repositorio Digital Institucional (UNCo)
collection Repositorio Digital Institucional (UNCo)
instname_str Universidad Nacional del Comahue
repository.name.fl_str_mv Repositorio Digital Institucional (UNCo) - Universidad Nacional del Comahue
repository.mail.fl_str_mv mirtha.mateo@biblioteca.uncoma.edu.ar; adriana.acuna@biblioteca.uncoma.edu.ar
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score 13.265058

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