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

Author

Listed:
  • Ndivhuwo Ndou

    (Department of Mathematics and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
    Department of Mathematical and Computational Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, 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)

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.

Suggested Citation

  • Ndivhuwo Ndou & Phumlani Dlamini & Byron Alexander Jacobs, 2024. "Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method," Mathematics, MDPI, vol. 12(7), pages 1-23, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1009-:d:1365679
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    References listed on IDEAS

    as
    1. Gurhan Gurarslan & Halil Karahan & Devrim Alkaya & Murat Sari & Mutlu Yasar, 2013. "Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, April.
    2. Mikhail K. Kolev & Miglena N. Koleva & Lubin G. Vulkov, 2022. "An Unconditional Positivity-Preserving Difference Scheme for Models of Cancer Migration and Invasion," Mathematics, MDPI, vol. 10(1), pages 1-22, January.
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    1. Gurhan Gurarslan, 2021. "Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters," Mathematics, MDPI, vol. 9(9), pages 1-14, May.

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