Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method
The processes of diffusion and reaction play essential roles in numerous system dynamics. Consequently, the solutions of reaction–diffusion equations have gained much attention because of not only their occurrence in many fields of science but also the existence of important properties and informati...
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| Format: | Article |
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De Gruyter
2020
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| _version_ | 1803629373378527232 |
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| author | Adeyeye, Oluwaseun Aldalbahi, Ali Raza, Jawad Omar, Zurni Rahaman, Mostafizur Rahimi-Gorji, Mohammad Hoang, Nguyen Minh |
| author_facet | Adeyeye, Oluwaseun Aldalbahi, Ali Raza, Jawad Omar, Zurni Rahaman, Mostafizur Rahimi-Gorji, Mohammad Hoang, Nguyen Minh |
| author_sort | Adeyeye, Oluwaseun |
| collection | UUM |
| description | The processes of diffusion and reaction play essential roles in numerous system dynamics. Consequently, the solutions of reaction–diffusion equations have gained much attention because of not only their occurrence in many fields of science but also the existence of important properties and information in the solutions. However, despite the wide range of numerical methods explored for approximating solutions, the adoption of block methods is yet to be investigated. Hence, this article introduces a new two-step third–fourth-derivative block method as a numerical approach to solve the reaction–diffusion equation. In order to ensure improved accuracy, the method introduces the concept of non linearity in the solution of the linear model through the presence of higher derivatives. The method obtained accurate solutions for the model at varying values of the dimensionless diffusion parameter and saturation parameter. Furthermore, the solutions are also in good agreement with previous solutions by existing authors. |
| first_indexed | 2024-07-04T06:36:49Z |
| format | Article |
| id | uum-27930 |
| institution | Universiti Utara Malaysia |
| last_indexed | 2024-07-04T06:36:49Z |
| publishDate | 2020 |
| publisher | De Gruyter |
| record_format | dspace |
| spelling | uum-279302020-11-30T01:20:07Z https://repo.uum.edu.my/id/eprint/27930/ Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method Adeyeye, Oluwaseun Aldalbahi, Ali Raza, Jawad Omar, Zurni Rahaman, Mostafizur Rahimi-Gorji, Mohammad Hoang, Nguyen Minh QA75 Electronic computers. Computer science The processes of diffusion and reaction play essential roles in numerous system dynamics. Consequently, the solutions of reaction–diffusion equations have gained much attention because of not only their occurrence in many fields of science but also the existence of important properties and information in the solutions. However, despite the wide range of numerical methods explored for approximating solutions, the adoption of block methods is yet to be investigated. Hence, this article introduces a new two-step third–fourth-derivative block method as a numerical approach to solve the reaction–diffusion equation. In order to ensure improved accuracy, the method introduces the concept of non linearity in the solution of the linear model through the presence of higher derivatives. The method obtained accurate solutions for the model at varying values of the dimensionless diffusion parameter and saturation parameter. Furthermore, the solutions are also in good agreement with previous solutions by existing authors. De Gruyter 2020 Article PeerReviewed Adeyeye, Oluwaseun and Aldalbahi, Ali and Raza, Jawad and Omar, Zurni and Rahaman, Mostafizur and Rahimi-Gorji, Mohammad and Hoang, Nguyen Minh (2020) Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method. International Journal of Nonlinear Sciences and Numerical Simulation, 1. ISSN 1565-1339 http://doi.org/10.1515/ijnsns-2019-0309 doi:10.1515/ijnsns-2019-0309 doi:10.1515/ijnsns-2019-0309 |
| spellingShingle | QA75 Electronic computers. Computer science Adeyeye, Oluwaseun Aldalbahi, Ali Raza, Jawad Omar, Zurni Rahaman, Mostafizur Rahimi-Gorji, Mohammad Hoang, Nguyen Minh Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method |
| title | Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method |
| title_full | Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method |
| title_fullStr | Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method |
| title_full_unstemmed | Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method |
| title_short | Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method |
| title_sort | nonlinear solution of the reaction diffusion equation using a two step third fourth derivative block method |
| topic | QA75 Electronic computers. Computer science |
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