Structure Preserving Numerical Analysis of Reaction-Diffusion Models
In this paper, we examine two structure preserving numerical finite difference methods for solving the various reaction-diffusion models in one dimension, appearing in chemistry and biology. These are the finite difference methods in splitting environment, namely, operator splitting nonstandard fini...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/5128343 |
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| _version_ | 1832551251973242880 |
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| author | Nauman Ahmed Muhammad Aziz-ur Rehman Waleed Adel Fahd Jarad Mubasher Ali Muhammad Rafiq Ali Akgül |
| author_facet | Nauman Ahmed Muhammad Aziz-ur Rehman Waleed Adel Fahd Jarad Mubasher Ali Muhammad Rafiq Ali Akgül |
| author_sort | Nauman Ahmed |
| collection | DOAJ |
| description | In this paper, we examine two structure preserving numerical finite difference methods for solving the various reaction-diffusion models in one dimension, appearing in chemistry and biology. These are the finite difference methods in splitting environment, namely, operator splitting nonstandard finite difference (OS-NSFD) methods that effectively deal with nonlinearity in the models and computationally efficient. Positivity of both the proposed splitting methods is proved mathematically and verified with the simulations. A comparison is made between proposed OS-NSFD methods and well-known classical operator splitting finite difference (OS-FD) methods, which demonstrates the advantages of proposed methods. Furthermore, we applied proposed NSFD splitting methods on several numerical examples to validate all the attributes of the proposed numerical designs. |
| format | Article |
| id | doaj-art-58d21a93c15c45138e2923ec77145831 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-58d21a93c15c45138e2923ec771458312025-02-03T06:01:51ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/5128343Structure Preserving Numerical Analysis of Reaction-Diffusion ModelsNauman Ahmed0Muhammad Aziz-ur Rehman1Waleed Adel2Fahd Jarad3Mubasher Ali4Muhammad Rafiq5Ali Akgül6Department of Mathematics and StatisticsDepartment of MathematicsDepartment of Mathematics and Engineering PhysicsDepartment of MathematicsSchool of Engineering and Digital ArtsDepartment of MathematicsSiirt UniversityIn this paper, we examine two structure preserving numerical finite difference methods for solving the various reaction-diffusion models in one dimension, appearing in chemistry and biology. These are the finite difference methods in splitting environment, namely, operator splitting nonstandard finite difference (OS-NSFD) methods that effectively deal with nonlinearity in the models and computationally efficient. Positivity of both the proposed splitting methods is proved mathematically and verified with the simulations. A comparison is made between proposed OS-NSFD methods and well-known classical operator splitting finite difference (OS-FD) methods, which demonstrates the advantages of proposed methods. Furthermore, we applied proposed NSFD splitting methods on several numerical examples to validate all the attributes of the proposed numerical designs.http://dx.doi.org/10.1155/2022/5128343 |
| spellingShingle | Nauman Ahmed Muhammad Aziz-ur Rehman Waleed Adel Fahd Jarad Mubasher Ali Muhammad Rafiq Ali Akgül Structure Preserving Numerical Analysis of Reaction-Diffusion Models Journal of Function Spaces |
| title | Structure Preserving Numerical Analysis of Reaction-Diffusion Models |
| title_full | Structure Preserving Numerical Analysis of Reaction-Diffusion Models |
| title_fullStr | Structure Preserving Numerical Analysis of Reaction-Diffusion Models |
| title_full_unstemmed | Structure Preserving Numerical Analysis of Reaction-Diffusion Models |
| title_short | Structure Preserving Numerical Analysis of Reaction-Diffusion Models |
| title_sort | structure preserving numerical analysis of reaction diffusion models |
| url | http://dx.doi.org/10.1155/2022/5128343 |
| work_keys_str_mv | AT naumanahmed structurepreservingnumericalanalysisofreactiondiffusionmodels AT muhammadazizurrehman structurepreservingnumericalanalysisofreactiondiffusionmodels AT waleedadel structurepreservingnumericalanalysisofreactiondiffusionmodels AT fahdjarad structurepreservingnumericalanalysisofreactiondiffusionmodels AT mubasherali structurepreservingnumericalanalysisofreactiondiffusionmodels AT muhammadrafiq structurepreservingnumericalanalysisofreactiondiffusionmodels AT aliakgul structurepreservingnumericalanalysisofreactiondiffusionmodels |