A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness

Tahira Sumbal Shaikh, Ali Akgül (), Muhammad Aziz-ur Rehman, Nauman Ahmed, Muhammad Sajid Iqbal, Naveed Shahid, Muhammad Rafiq and Manuel De la Sen
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Tahira Sumbal Shaikh: Department of Mathematics, Lahore College for Women University, Lahore 54600, Pakistan
Ali Akgül: Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, Lebanon
Muhammad Aziz-ur Rehman: Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
Nauman Ahmed: Department of Mathematics, Lahore College for Women University, Lahore 54600, Pakistan
Muhammad Sajid Iqbal: Department of Humanities & Basic Sciences, MCS, National University of Sciences and Technology, Islamabad 44000, Pakistan
Naveed Shahid: Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan
Muhammad Rafiq: Mathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard, Nicosia 99138, Turkey
Manuel De la Sen: Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Spain

Mathematics, 2022, vol. 11, issue 1, 1-17

Abstract: 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.

Keywords: optimal solution; auxiliary data; advection; equilibrium point; glycolysis; diffusion; structure preserving (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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