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Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method

  • Oluwaseun Adeyeye , Ali Aldalbahi , Jawad Raza , Zurni Omar , Mostafizur Rahaman , Mohammad Rahimi-Gorji and Nguyen Minh Hoang EMAIL logo
Published/Copyright: September 16, 2020

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.


Corresponding author: Nguyen Minh Hoang, Institute of Research and Development, Duy Tan University, Danang 550000, Viet Nam, E-mail:

Funding source: King Saud University

Award Identifier / Grant number: RSP-2020/30

Acknowledgement

The authors acknowledge King Saud University, Riyadh, Saudi Arabia, for funding this work through Researchers Supporting Project number (RSP-2020/30).

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The authors acknowledge King Saud University, Riyadh, Saudi Arabia, for funding this work through Researchers Supporting Project number (RSP-2020/30).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2019-12-28
Accepted: 2020-08-08
Published Online: 2020-09-16
Published in Print: 2021-02-23

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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