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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IEEE
2019-01-01
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Series: | IEEE Access |
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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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format | Article |
id | doaj.art-7befa1a872264eb0945bf05c7c621aa8 |
institution | Directory Open Access Journal |
issn | 2169-3536 |
language | English |
last_indexed | 2024-12-13T23:53:09Z |
publishDate | 2019-01-01 |
publisher | IEEE |
record_format | Article |
series | IEEE Access |
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/ |
work_keys_str_mv | AT shahidhasnain numericalstudytocoupledthreedimensionalreactiondiffusionsystem AT muhammadsaqib numericalstudytocoupledthreedimensionalreactiondiffusionsystem AT muhammadfafzaal numericalstudytocoupledthreedimensionalreactiondiffusionsystem AT iqtadarhussain numericalstudytocoupledthreedimensionalreactiondiffusionsystem |