Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method

Ndou, Ndivhuwo; Dlamini, Phumlani; Jacobs, Byron Alexander

doi:10.3390/math12071009

Open AccessArticle

Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method

by

Ndivhuwo Ndou

^1,2,*

,

Phumlani Dlamini

¹ and

Byron Alexander Jacobs

¹

Department of Mathematics and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa

²

Department of Mathematical and Computational Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

^*

Author to whom correspondence should be addressed.

Mathematics 2024, 12(7), 1009; https://doi.org/10.3390/math12071009

Submission received: 20 February 2024 / Revised: 18 March 2024 / Accepted: 22 March 2024 / Published: 28 March 2024

(This article belongs to the Section E: Applied Mathematics)

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Abstract

In this paper, the enhanced higher-order unconditionally positive finite difference method is developed to solve the linear, non-linear and system advection diffusion reaction equations. Investigation into the effectiveness and efficiency of the proposed method is carried out by calculating the convergence rate, error and computational time. A comparison of the solutions obtained by the enhanced higher-order unconditionally positive finite difference and exact solution is conducted for validation purposes. The numerical results show that the developed method reduced the time taken to solve the linear and non-linear advection diffusion reaction equations as compared to the results obtained by the higher-order unconditionally positive finite difference method.

Keywords: enhanced higher-order unconditionally positive finite difference method; unconditionally positive finite difference method; advection diffusion reaction equations; von Neumann stability analysis; consistency; stability analysis

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MDPI and ACS Style

Ndou, N.; Dlamini, P.; Jacobs, B.A. Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method. Mathematics 2024, 12, 1009. https://doi.org/10.3390/math12071009

AMA Style

Ndou N, Dlamini P, Jacobs BA. Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method. Mathematics. 2024; 12(7):1009. https://doi.org/10.3390/math12071009

Chicago/Turabian Style

Ndou, Ndivhuwo, Phumlani Dlamini, and Byron Alexander Jacobs. 2024. "Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method" Mathematics 12, no. 7: 1009. https://doi.org/10.3390/math12071009

APA Style

Ndou, N., Dlamini, P., & Jacobs, B. A. (2024). Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method. Mathematics, 12(7), 1009. https://doi.org/10.3390/math12071009

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Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method

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