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

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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 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.

Item Type:	Article
Uncontrolled Keywords:	block method; reaction–diffusion equation; two-step third–fourth-derivative
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions:	School of Quantitative Sciences
Depositing User:	Mrs. Norazmilah Yaakub
Date Deposited:	30 Nov 2020 01:20
Last Modified:	30 Nov 2020 01:20
URI:	https://repo.uum.edu.my/id/eprint/27930

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