Approximation of the modified error function

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 orig...

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Autores principales: Ceretani, Andrea Noemí, Salva, Natalia Nieves, Tarzia, Domingo Alberto
Formato: Articulo article acceptedVersion
Lenguaje:Inglés
Publicado: Elsevier 2018
Materias:
Modified error function
Error function
Phase change problem
Temperature dependent thermal
Conductivity
Nonlinear second order ordinary differential equation
Ciencias Aplicadas
Acceso en línea:http://rdi.uncoma.edu.ar/handle/uncomaid/17308
Aporte de:
Repositorio Institucional UNCo de Universidad Nacional del Comahue
id I22-R178-uncomaid-17308
record_format dspace
spelling I22-R178-uncomaid-173082023-10-11T14:49:18Z Approximation of the modified error function Ceretani, Andrea Noemí Salva, Natalia Nieves Tarzia, Domingo Alberto Modified error function Error function Phase change problem Temperature dependent thermal Conductivity Nonlinear second order ordinary differential equation Ciencias Aplicadas 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 2018-11-15 2023-07-04T14:17:33Z 2023-07-04T14:17:33Z Articulo article acceptedVersion 0096-3003 http://rdi.uncoma.edu.ar/handle/uncomaid/17308 eng https://doi.org/10.1016/j.amc.2018.05.054 Atribución-NoComercial-CompartirIgual 2.5 Argentina https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ application/pdf pp. 607-617 application/pdf Elsevier Applied Mathematics and Computation. Vol. 337 (2018)
institution Universidad Nacional del Comahue
institution_str I-22
repository_str R-178
collection Repositorio Institucional UNCo
language Inglés
topic Modified error function
Error function
Phase change problem
Temperature dependent thermal
Conductivity
Nonlinear second order ordinary differential equation
Ciencias Aplicadas
spellingShingle Modified error function
Error function
Phase change problem
Temperature dependent thermal
Conductivity
Nonlinear second order ordinary differential equation
Ciencias Aplicadas
Ceretani, Andrea Noemí
Salva, Natalia Nieves
Tarzia, Domingo Alberto
Approximation of the modified error function
topic_facet Modified error function
Error function
Phase change problem
Temperature dependent thermal
Conductivity
Nonlinear second order ordinary differential equation
Ciencias Aplicadas
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.
format Articulo
article
acceptedVersion
author Ceretani, Andrea Noemí
Salva, Natalia Nieves
Tarzia, Domingo Alberto
author_facet Ceretani, Andrea Noemí
Salva, Natalia Nieves
Tarzia, Domingo Alberto
author_sort Ceretani, Andrea Noemí
title Approximation of the modified error function
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
publisher Elsevier
publishDate 2018
url http://rdi.uncoma.edu.ar/handle/uncomaid/17308
work_keys_str_mv AT ceretaniandreanoemi approximationofthemodifiederrorfunction
AT salvanatalianieves approximationofthemodifiederrorfunction
AT tarziadomingoalberto approximationofthemodifiederrorfunction
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