A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution

This paper proposes a higher-order numerical approximation scheme to solve singularly perturbed reaction–diffusion boundary value problems. The proposed scheme is a combination of a fourth-order numerical difference method and classical central difference method applied on a non-equidistant grid. Th...

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Autores principales:	Aastha Gupta, Aditya Kaushik
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Singular perturbation Boundary value problems Higher-order approximation Grid equidistribution Robust discretization Hybrid difference scheme Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/e73f847ea7d24c98a5121ef5e71dbab5
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id	oai:doaj.org-article:e73f847ea7d24c98a5121ef5e71dbab5
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spelling	oai:doaj.org-article:e73f847ea7d24c98a5121ef5e71dbab52021-11-22T04:22:48ZA higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution2090-447910.1016/j.asej.2021.04.024https://doaj.org/article/e73f847ea7d24c98a5121ef5e71dbab52021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2090447921002124https://doaj.org/toc/2090-4479This paper proposes a higher-order numerical approximation scheme to solve singularly perturbed reaction–diffusion boundary value problems. The proposed scheme is a combination of a fourth-order numerical difference method and classical central difference method applied on a non-equidistant grid. The non-equidistant grid is generated by equi-distributing a non-negative monitor function. The theoretical and empirical error analysis demonstrate that the proposed scheme has fourth-order uniform convergence with respect to the perturbation parameter.Aastha GuptaAditya KaushikElsevierarticleSingular perturbationBoundary value problemsHigher-order approximationGrid equidistributionRobust discretizationHybrid difference schemeEngineering (General). Civil engineering (General)TA1-2040ENAin Shams Engineering Journal, Vol 12, Iss 4, Pp 4211-4221 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Singular perturbation Boundary value problems Higher-order approximation Grid equidistribution Robust discretization Hybrid difference scheme Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Singular perturbation Boundary value problems Higher-order approximation Grid equidistribution Robust discretization Hybrid difference scheme Engineering (General). Civil engineering (General) TA1-2040 Aastha Gupta Aditya Kaushik A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution
description	This paper proposes a higher-order numerical approximation scheme to solve singularly perturbed reaction–diffusion boundary value problems. The proposed scheme is a combination of a fourth-order numerical difference method and classical central difference method applied on a non-equidistant grid. The non-equidistant grid is generated by equi-distributing a non-negative monitor function. The theoretical and empirical error analysis demonstrate that the proposed scheme has fourth-order uniform convergence with respect to the perturbation parameter.
format	article
author	Aastha Gupta Aditya Kaushik
author_facet	Aastha Gupta Aditya Kaushik
author_sort	Aastha Gupta
title	A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution
title_short	A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution
title_full	A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution
title_fullStr	A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution
title_full_unstemmed	A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution
title_sort	higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/e73f847ea7d24c98a5121ef5e71dbab5
work_keys_str_mv	AT aasthagupta ahigherorderaccuratedifferenceapproximationofsingularlyperturbedreactiondiffusionproblemusinggridequidistribution AT adityakaushik ahigherorderaccuratedifferenceapproximationofsingularlyperturbedreactiondiffusionproblemusinggridequidistribution AT aasthagupta higherorderaccuratedifferenceapproximationofsingularlyperturbedreactiondiffusionproblemusinggridequidistribution AT adityakaushik higherorderaccuratedifferenceapproximationofsingularlyperturbedreactiondiffusionproblemusinggridequidistribution
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A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution

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