Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard

The study of biofilm formation is undoubtedly important due to micro-organisms forming a protected mode from the host defense mechanism, which may result in alteration in the host gene transcription and growth rate. A mathematical model of the nonlinear advection–diffusion–reaction equation has been...

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Autores principales:	Yusuf Olatunji Tijani, Appanah Rao Appadu, Adebayo Abiodun Aderogba
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	biofilm non-standard finite difference advection–diffusion–reaction positivity Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/48675ecae24c4897bda5f39ba3926c7b
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spelling	oai:doaj.org-article:48675ecae24c4897bda5f39ba3926c7b2021-11-25T17:17:18ZSome Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard10.3390/computation91101232079-3197https://doaj.org/article/48675ecae24c4897bda5f39ba3926c7b2021-11-01T00:00:00Zhttps://www.mdpi.com/2079-3197/9/11/123https://doaj.org/toc/2079-3197The study of biofilm formation is undoubtedly important due to micro-organisms forming a protected mode from the host defense mechanism, which may result in alteration in the host gene transcription and growth rate. A mathematical model of the nonlinear advection–diffusion–reaction equation has been studied for biofilm formation. In this paper, we present two novel non-standard finite difference schemes to obtain an approximate solution to the mathematical model of biofilm formation. One explicit non-standard finite difference scheme is proposed for biomass density equation and one property-conserving scheme for a coupled substrate–biomass system of equations. The nonlinear term in the mathematical model has been handled efficiently. The proposed schemes maintain dynamical consistency (positivity, boundedness, merging of colonies, biofilm annihilation), which is revealed through experimental observation. In order to verify the accuracy and effectiveness of our proposed schemes, we compare our results with those obtained from standard finite difference schemes and earlier known results in the literature. The proposed schemes (NSFD1 and NSFD2) show good performance. The NSFD2 scheme reveals that the processes of biofilm formation and nutritive substrate growth are intricately linked.Yusuf Olatunji TijaniAppanah Rao AppaduAdebayo Abiodun AderogbaMDPI AGarticlebiofilmnon-standard finite differenceadvection–diffusion–reactionpositivityElectronic computers. Computer scienceQA75.5-76.95ENComputation, Vol 9, Iss 123, p 123 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	biofilm non-standard finite difference advection–diffusion–reaction positivity Electronic computers. Computer science QA75.5-76.95
spellingShingle	biofilm non-standard finite difference advection–diffusion–reaction positivity Electronic computers. Computer science QA75.5-76.95 Yusuf Olatunji Tijani Appanah Rao Appadu Adebayo Abiodun Aderogba Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard
description	The study of biofilm formation is undoubtedly important due to micro-organisms forming a protected mode from the host defense mechanism, which may result in alteration in the host gene transcription and growth rate. A mathematical model of the nonlinear advection–diffusion–reaction equation has been studied for biofilm formation. In this paper, we present two novel non-standard finite difference schemes to obtain an approximate solution to the mathematical model of biofilm formation. One explicit non-standard finite difference scheme is proposed for biomass density equation and one property-conserving scheme for a coupled substrate–biomass system of equations. The nonlinear term in the mathematical model has been handled efficiently. The proposed schemes maintain dynamical consistency (positivity, boundedness, merging of colonies, biofilm annihilation), which is revealed through experimental observation. In order to verify the accuracy and effectiveness of our proposed schemes, we compare our results with those obtained from standard finite difference schemes and earlier known results in the literature. The proposed schemes (NSFD1 and NSFD2) show good performance. The NSFD2 scheme reveals that the processes of biofilm formation and nutritive substrate growth are intricately linked.
format	article
author	Yusuf Olatunji Tijani Appanah Rao Appadu Adebayo Abiodun Aderogba
author_facet	Yusuf Olatunji Tijani Appanah Rao Appadu Adebayo Abiodun Aderogba
author_sort	Yusuf Olatunji Tijani
title	Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard
title_short	Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard
title_full	Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard
title_fullStr	Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard
title_full_unstemmed	Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard
title_sort	some finite difference methods to model biofilm growth and decay: classical and non-standard
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/48675ecae24c4897bda5f39ba3926c7b
work_keys_str_mv	AT yusufolatunjitijani somefinitedifferencemethodstomodelbiofilmgrowthanddecayclassicalandnonstandard AT appanahraoappadu somefinitedifferencemethodstomodelbiofilmgrowthanddecayclassicalandnonstandard AT adebayoabiodunaderogba somefinitedifferencemethodstomodelbiofilmgrowthanddecayclassicalandnonstandard
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Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard

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