A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness
In this article, a nonlinear autocatalytic chemical reaction glycolysis model with the appearance of advection and diffusion is proposed. The occurrence and unicity of the solutions in Banach spaces are investigated. The solutions to these types of models are obtained by the optimization of the clos...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/1/37 |
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| author | Tahira Sumbal Shaikh Ali Akgül Muhammad Aziz-ur Rehman Nauman Ahmed Muhammad Sajid Iqbal Naveed Shahid Muhammad Rafiq Manuel De la Sen |
| author_facet | Tahira Sumbal Shaikh Ali Akgül Muhammad Aziz-ur Rehman Nauman Ahmed Muhammad Sajid Iqbal Naveed Shahid Muhammad Rafiq Manuel De la Sen |
| author_sort | Tahira Sumbal Shaikh |
| collection | DOAJ |
| description | In this article, a nonlinear autocatalytic chemical reaction glycolysis model with the appearance of advection and diffusion is proposed. The occurrence and unicity of the solutions in Banach spaces are investigated. The solutions to these types of models are obtained by the optimization of the closed and convex subsets of the function space. Explicit estimates of the solutions for the admissible auxiliary data are formulated. An elegant numerical scheme is designed for an autocatalytic chemical reaction model, that is, the glycolysis model. The fundamental traits of the prescribed numerical method, for instance, the positivity, consistency, stability, etc., are also verified. The authenticity of the proposed scheme is ensured by comparing it with two extensively used numerical techniques. A numerical example is presented to observe the graphical behavior of the continuous system by constructing the numerical algorithm. The comparison depicts that the projected numerical design is more productive as compared to the other two schemes, as it holds all the important properties of the continuous model. |
| first_indexed | 2024-03-11T09:54:43Z |
| format | Article |
| id | doaj.art-253b42b1e467488c93c9bd6dab64584c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:54:43Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-253b42b1e467488c93c9bd6dab64584c2023-11-16T15:52:33ZengMDPI AGMathematics2227-73902022-12-011113710.3390/math11010037A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and UniquenessTahira Sumbal Shaikh0Ali Akgül1Muhammad Aziz-ur Rehman2Nauman Ahmed3Muhammad Sajid Iqbal4Naveed Shahid5Muhammad Rafiq6Manuel De la Sen7Department of Mathematics, Lahore College for Women University, Lahore 54600, PakistanDepartment of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, LebanonDepartment of Mathematics, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, Lahore College for Women University, Lahore 54600, PakistanDepartment of Humanities & Basic Sciences, MCS, National University of Sciences and Technology, Islamabad 44000, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore 54590, PakistanMathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard, Nicosia 99138, TurkeyDepartment of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, SpainIn this article, a nonlinear autocatalytic chemical reaction glycolysis model with the appearance of advection and diffusion is proposed. The occurrence and unicity of the solutions in Banach spaces are investigated. The solutions to these types of models are obtained by the optimization of the closed and convex subsets of the function space. Explicit estimates of the solutions for the admissible auxiliary data are formulated. An elegant numerical scheme is designed for an autocatalytic chemical reaction model, that is, the glycolysis model. The fundamental traits of the prescribed numerical method, for instance, the positivity, consistency, stability, etc., are also verified. The authenticity of the proposed scheme is ensured by comparing it with two extensively used numerical techniques. A numerical example is presented to observe the graphical behavior of the continuous system by constructing the numerical algorithm. The comparison depicts that the projected numerical design is more productive as compared to the other two schemes, as it holds all the important properties of the continuous model.https://www.mdpi.com/2227-7390/11/1/37optimal solutionauxiliary dataadvectionequilibrium pointglycolysisdiffusion |
| spellingShingle | Tahira Sumbal Shaikh Ali Akgül Muhammad Aziz-ur Rehman Nauman Ahmed Muhammad Sajid Iqbal Naveed Shahid Muhammad Rafiq Manuel De la Sen A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness Mathematics optimal solution auxiliary data advection equilibrium point glycolysis diffusion |
| title | A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness |
| title_full | A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness |
| title_fullStr | A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness |
| title_full_unstemmed | A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness |
| title_short | A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness |
| title_sort | nonlinear structure of a chemical reaction model and numerical modeling with the new aspect of existence and uniqueness |
| topic | optimal solution auxiliary data advection equilibrium point glycolysis diffusion |
| url | https://www.mdpi.com/2227-7390/11/1/37 |
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