Numerical Study to Coupled Three Dimensional Reaction Diffusion System

The numerical solution of reaction diffusion systems may require more computational efforts if the change in concentrations occurs extremely rapid. This is because more time points are needed to resolve the reaction diffusion process accurately. In this paper, three finite difference implicit scheme...

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Main Authors: shahid Hasnain, Muhammad Saqib, Muhammad F. Afzaal, Iqtadar Hussain
Format: Article
Language:English
Published: IEEE 2019-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/8674554/
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author shahid Hasnain
Muhammad Saqib
Muhammad F. Afzaal
Iqtadar Hussain
author_facet shahid Hasnain
Muhammad Saqib
Muhammad F. Afzaal
Iqtadar Hussain
author_sort shahid Hasnain
collection DOAJ
description The numerical solution of reaction diffusion systems may require more computational efforts if the change in concentrations occurs extremely rapid. This is because more time points are needed to resolve the reaction diffusion process accurately. In this paper, three finite difference implicit schemes are used which are unconditionally stable in order to enhance consistency. Novelty is reported by compact finite difference implicit scheme on a reaction diffusion system with higher accuracy measured by $L_{2}, L_{\infty }$ , and $Relative_{error}$ norms. Efficiency is observed by reducing grid space along small temporal steps. CPU performance, transmission capacity along comparison of three schemes shows excellent agreement with the analytical solution.
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spelling doaj.art-7befa1a872264eb0945bf05c7c621aa82022-12-21T23:26:42ZengIEEEIEEE Access2169-35362019-01-017466954670510.1109/ACCESS.2019.29039778674554Numerical Study to Coupled Three Dimensional Reaction Diffusion Systemshahid Hasnain0https://orcid.org/0000-0002-8069-3075Muhammad Saqib1https://orcid.org/0000-0002-4144-5570Muhammad F. Afzaal2Iqtadar Hussain3Department of Physics and Applied Mathematics (DPAM), Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore, PakistanDepartment of Mathematics, Air University, Islamabad, PakistanSchool of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, ChinaDepartment of Mathematics, Statistics and Physics, Qatar University, Doha, QatarThe numerical solution of reaction diffusion systems may require more computational efforts if the change in concentrations occurs extremely rapid. This is because more time points are needed to resolve the reaction diffusion process accurately. In this paper, three finite difference implicit schemes are used which are unconditionally stable in order to enhance consistency. Novelty is reported by compact finite difference implicit scheme on a reaction diffusion system with higher accuracy measured by $L_{2}, L_{\infty }$ , and $Relative_{error}$ norms. Efficiency is observed by reducing grid space along small temporal steps. CPU performance, transmission capacity along comparison of three schemes shows excellent agreement with the analytical solution.https://ieeexplore.ieee.org/document/8674554/Reaction diffusion systemsalternating direction implicitDouglas schemehigher order compact schemeThomas algorithm
spellingShingle shahid Hasnain
Muhammad Saqib
Muhammad F. Afzaal
Iqtadar Hussain
Numerical Study to Coupled Three Dimensional Reaction Diffusion System
IEEE Access
Reaction diffusion systems
alternating direction implicit
Douglas scheme
higher order compact scheme
Thomas algorithm
title Numerical Study to Coupled Three Dimensional Reaction Diffusion System
title_full Numerical Study to Coupled Three Dimensional Reaction Diffusion System
title_fullStr Numerical Study to Coupled Three Dimensional Reaction Diffusion System
title_full_unstemmed Numerical Study to Coupled Three Dimensional Reaction Diffusion System
title_short Numerical Study to Coupled Three Dimensional Reaction Diffusion System
title_sort numerical study to coupled three dimensional reaction diffusion system
topic Reaction diffusion systems
alternating direction implicit
Douglas scheme
higher order compact scheme
Thomas algorithm
url https://ieeexplore.ieee.org/document/8674554/
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AT muhammadsaqib numericalstudytocoupledthreedimensionalreactiondiffusionsystem
AT muhammadfafzaal numericalstudytocoupledthreedimensionalreactiondiffusionsystem
AT iqtadarhussain numericalstudytocoupledthreedimensionalreactiondiffusionsystem