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

Ndivhuwo Ndou (), Phumlani Dlamini and Byron Alexander Jacobs
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Ndivhuwo Ndou: Department of Mathematics and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
Phumlani Dlamini: Department of Mathematics and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
Byron Alexander Jacobs: Department of Mathematics and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa

Mathematics, 2024, vol. 12, issue 7, 1-23

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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