Numerical solution for interval initial value problems based on interactive arithmetic
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.22111/ijfs.2022.7206 http://hdl.handle.net/11449/246239 |
Resumo: | This work studies Interval Initial Value Problems (IIVPs), where the derivative is given by the generalized Hukuhara derivative (gH-derivative) and the initial condition is given by an interval. The focus of the paper is to provide the numerical approximations for the solutions associated with the gH-derivative of IIVPs. This article considers the Euler numerical method, where the classical arithmetic operation is adapted for intervals. The arithmetic considered here is obtained using sup-J extension principle, where J is a particular family of joint possibility distributions. This family gives raise to different types of interactivity and this work shows what kind of interactivity is necessary in the numerical method, in order to approximate the solution via gH-derivative. To illustrate the results, the paper focuses in the decay Malthusian model. |
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Numerical solution for interval initial value problems based on interactive arithmeticeuler methodgeneralized hukuhara derivativeinteractivityInterval initial value problemmalthusian modelThis work studies Interval Initial Value Problems (IIVPs), where the derivative is given by the generalized Hukuhara derivative (gH-derivative) and the initial condition is given by an interval. The focus of the paper is to provide the numerical approximations for the solutions associated with the gH-derivative of IIVPs. This article considers the Euler numerical method, where the classical arithmetic operation is adapted for intervals. The arithmetic considered here is obtained using sup-J extension principle, where J is a particular family of joint possibility distributions. This family gives raise to different types of interactivity and this work shows what kind of interactivity is necessary in the numerical method, in order to approximate the solution via gH-derivative. To illustrate the results, the paper focuses in the decay Malthusian model.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computing University of CampinasIlum School of Science Brazilian Center for Research in Energy and MaterialsDepartment of Mathematics Sȁo Paulo State UniversityCAPES: 001CNPq: 313313/2020-2CNPq: 314885/2021-8Universidade Estadual de Campinas (UNICAMP)Brazilian Center for Research in Energy and MaterialsSȁo Paulo State UniversityEsmi, E.Sacilotto, C.Wasques, V. F.Barros, L. C.2023-07-29T12:35:30Z2023-07-29T12:35:30Z2022-11-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1-12http://dx.doi.org/10.22111/ijfs.2022.7206Iranian Journal of Fuzzy Systems, v. 19, n. 6, p. 1-12, 2022.2676-43341735-0654http://hdl.handle.net/11449/24623910.22111/ijfs.2022.72062-s2.0-85141383337Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengIranian Journal of Fuzzy Systemsinfo:eu-repo/semantics/openAccess2023-07-29T12:35:30Zoai:repositorio.unesp.br:11449/246239Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-07-29T12:35:30Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Numerical solution for interval initial value problems based on interactive arithmetic |
title |
Numerical solution for interval initial value problems based on interactive arithmetic |
spellingShingle |
Numerical solution for interval initial value problems based on interactive arithmetic Esmi, E. euler method generalized hukuhara derivative interactivity Interval initial value problem malthusian model |
title_short |
Numerical solution for interval initial value problems based on interactive arithmetic |
title_full |
Numerical solution for interval initial value problems based on interactive arithmetic |
title_fullStr |
Numerical solution for interval initial value problems based on interactive arithmetic |
title_full_unstemmed |
Numerical solution for interval initial value problems based on interactive arithmetic |
title_sort |
Numerical solution for interval initial value problems based on interactive arithmetic |
author |
Esmi, E. |
author_facet |
Esmi, E. Sacilotto, C. Wasques, V. F. Barros, L. C. |
author_role |
author |
author2 |
Sacilotto, C. Wasques, V. F. Barros, L. C. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual de Campinas (UNICAMP) Brazilian Center for Research in Energy and Materials Sȁo Paulo State University |
dc.contributor.author.fl_str_mv |
Esmi, E. Sacilotto, C. Wasques, V. F. Barros, L. C. |
dc.subject.por.fl_str_mv |
euler method generalized hukuhara derivative interactivity Interval initial value problem malthusian model |
topic |
euler method generalized hukuhara derivative interactivity Interval initial value problem malthusian model |
description |
This work studies Interval Initial Value Problems (IIVPs), where the derivative is given by the generalized Hukuhara derivative (gH-derivative) and the initial condition is given by an interval. The focus of the paper is to provide the numerical approximations for the solutions associated with the gH-derivative of IIVPs. This article considers the Euler numerical method, where the classical arithmetic operation is adapted for intervals. The arithmetic considered here is obtained using sup-J extension principle, where J is a particular family of joint possibility distributions. This family gives raise to different types of interactivity and this work shows what kind of interactivity is necessary in the numerical method, in order to approximate the solution via gH-derivative. To illustrate the results, the paper focuses in the decay Malthusian model. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-11-01 2023-07-29T12:35:30Z 2023-07-29T12:35:30Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.22111/ijfs.2022.7206 Iranian Journal of Fuzzy Systems, v. 19, n. 6, p. 1-12, 2022. 2676-4334 1735-0654 http://hdl.handle.net/11449/246239 10.22111/ijfs.2022.7206 2-s2.0-85141383337 |
url |
http://dx.doi.org/10.22111/ijfs.2022.7206 http://hdl.handle.net/11449/246239 |
identifier_str_mv |
Iranian Journal of Fuzzy Systems, v. 19, n. 6, p. 1-12, 2022. 2676-4334 1735-0654 10.22111/ijfs.2022.7206 2-s2.0-85141383337 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Iranian Journal of Fuzzy Systems |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1-12 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799964873475489792 |