High order nonstandard finite-difference methods

Nonstandard finite difference (NSFD) methods have been considered to overcome some issues of standard methods, particularly when the numerical solution must preserve important properties of the exact solution. These issues increase for high order methods. In this paper we first derive a general proc...

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Detalles Bibliográficos
Autores: Conte, Dajana, Pagano, Giovanni, Roldán Marrodán, Teodoro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2026
País:España
Institución:Universidad San Jorge (USJ)
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/55361
Acceso en línea:https://hdl.handle.net/2454/55361
Access Level:acceso abierto
Palabra clave:Nonstandard finite differences
High order of convergence
Unconditional positivity
Elementary stability
Initial value problems
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spelling High order nonstandard finite-difference methodsConte, DajanaPagano, GiovanniRoldán Marrodán, TeodoroNonstandard finite differencesHigh order of convergenceUnconditional positivityElementary stabilityInitial value problemsNonstandard finite difference (NSFD) methods have been considered to overcome some issues of standard methods, particularly when the numerical solution must preserve important properties of the exact solution. These issues increase for high order methods. In this paper we first derive a general procedure to obtain unconditionally positive second order NSFD methods. Furthermore, by suitably adding some parameters within these schemes, we show that it is still possible to get positivity, and also to preserve other qualitative properties of the exact solution. In fact, for each particular problem we can get optimal values of that guarantee positivity, elementary stability and the minimization of the local truncation error, being possible to achieve also third order nonstandard schemes, which are not present in the literature. As an example of use, we employ the developed theory to derive positive and elementary stable NSFD methods of order one, two and three for a predator-prey model, showing their advantages over other nonstandard methods from the literature.This work has been supported by GNCS-INdAM projects and by the Italian Ministry of University and Research (MUR), through the PRIN PNRR 2022 project P20228C2PP (CUP: F53D23010020001) BAT-MEN (BATtery Modeling, Experiments & Numerics). This work has also been supported by the Spanish Ministerio de Econom\u00EDa y Competividad through the Project PID2022-141385NB-I00.ElsevierEstadística, Informática y MatemáticasEstatistika, Informatika eta MatematikaInstitute for Advanced Materials and Mathematics - INAMAT22026info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/55361reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad San Jorge (USJ)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-141385NB-I00© 2025 The Author(s). This is an open access article under the CC BY-NC-ND license.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/553612026-06-17T12:41:47Z
dc.title.none.fl_str_mv High order nonstandard finite-difference methods
title High order nonstandard finite-difference methods
spellingShingle High order nonstandard finite-difference methods
Conte, Dajana
Nonstandard finite differences
High order of convergence
Unconditional positivity
Elementary stability
Initial value problems
title_short High order nonstandard finite-difference methods
title_full High order nonstandard finite-difference methods
title_fullStr High order nonstandard finite-difference methods
title_full_unstemmed High order nonstandard finite-difference methods
title_sort High order nonstandard finite-difference methods
dc.creator.none.fl_str_mv Conte, Dajana
Pagano, Giovanni
Roldán Marrodán, Teodoro
author Conte, Dajana
author_facet Conte, Dajana
Pagano, Giovanni
Roldán Marrodán, Teodoro
author_role author
author2 Pagano, Giovanni
Roldán Marrodán, Teodoro
author2_role author
author
dc.contributor.none.fl_str_mv Estadística, Informática y Matemáticas
Estatistika, Informatika eta Matematika
Institute for Advanced Materials and Mathematics - INAMAT2
dc.subject.none.fl_str_mv Nonstandard finite differences
High order of convergence
Unconditional positivity
Elementary stability
Initial value problems
topic Nonstandard finite differences
High order of convergence
Unconditional positivity
Elementary stability
Initial value problems
description Nonstandard finite difference (NSFD) methods have been considered to overcome some issues of standard methods, particularly when the numerical solution must preserve important properties of the exact solution. These issues increase for high order methods. In this paper we first derive a general procedure to obtain unconditionally positive second order NSFD methods. Furthermore, by suitably adding some parameters within these schemes, we show that it is still possible to get positivity, and also to preserve other qualitative properties of the exact solution. In fact, for each particular problem we can get optimal values of that guarantee positivity, elementary stability and the minimization of the local truncation error, being possible to achieve also third order nonstandard schemes, which are not present in the literature. As an example of use, we employ the developed theory to derive positive and elementary stable NSFD methods of order one, two and three for a predator-prey model, showing their advantages over other nonstandard methods from the literature.
publishDate 2026
dc.date.none.fl_str_mv 2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/55361
url https://hdl.handle.net/2454/55361
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-141385NB-I00
dc.rights.none.fl_str_mv © 2025 The Author(s). This is an open access article under the CC BY-NC-ND license.
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2025 The Author(s). This is an open access article under the CC BY-NC-ND license.
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad San Jorge (USJ)
instname_str Universidad San Jorge (USJ)
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
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