Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method
Author:
Adeyeye Oluwaseun1, Aldalbahi Ali2, Raza Jawad3, Omar Zurni1, Rahaman Mostafizur2, Rahimi-Gorji Mohammad4, Hoang Nguyen Minh5
Affiliation:
1. School of Quantitative Sciences, Universiti Utara Malaysia Sintok 06010 , Kedah , Malaysia 2. Department of Chemistry , College of Science, King Saud University , Riyadh 11451 , Saudi Arabia 3. Department of Mathematics & Statistics , Institute of Southern Punjab (ISP) , Punjab , Pakistan 4. Faculty of Medicine and Health Sciences, Ghent University , 9000 Gent , Belgium 5. Institute of Research and Development, Duy Tan University , Danang 550000 , Viet Nam
Abstract
Abstract
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 nonlinearity 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.
Funder
King Saud University
Publisher
Walter de Gruyter GmbH
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modelling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics
Reference38 articles.
1. L. T. Villa, N. A. Acosta, and C. M. Albarracin, “A note on non-isothermal diffusion-reaction processes,” Int. J. Pure Appl. Math., vol. 71, no. 4, pp. 525–538, 2011. Corpus ID: 124040441. 2. D. Bedeaux, I. Pagonabarraga, J. O. De Zárate, J. V. Sengers, and S. Kjelstrup, “Mesoscopic non-equilibrium thermodynamics of non-isothermal reaction–diffusion,” Phys. Chem. Chem. Phys., vol. 12, no. 39, pp. 12780–12793, 2010. https://doi.org/10.1039/c0cp00289e. 3. G. F. Froment, K. B. Bischoff, and J. De Wilde, Chemical Reactor Analysis and Design, vol. 2, New York, Wiley, 1990. 4. S. Kjelstrup, J. M. Rubi, and D. Bedeaux, “Energy dissipation in slipping biological pumps,” Phys. Chem. Chem. Phys., vol. 7, no. 23, pp. 4009–4018, 2005. https://doi.org/10.1039/b511990a. 5. A. S. Blix, Arctic Animals and their Adaptations to Life on the Edge, Bergen, Norway, Tapir Academic Press, 2005.
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