Non-Standard Discretization of the Advection-Diffusion-Reaction Equation with Logistic Growth Reaction

Authors

  • Guy Phares Fotso Fotso National committee for Development of Technologies, MINRESI, P. O. Box 1457, Yaoundé, Cameroon, Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon
  • Balkissou Hamidou National committee for Development of Technologies, MINRESI, P. O. Box 1457, Yaoundé, Cameroon,Department of Physics, University of Ngaoundéré, P. O. Box 454, Ngaoundéré, Cameroon
  • Achille Landri Pokam Kakeu Research Laboratory in Geodesy, National Institute of Cartography, MINRESI, P. O. Box 1457, Yaoundé, Cameroon,Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon

Keywords:

Non-standard finite difference methods, CFL stability, advection-diffusion-reaction equation, logistic equation, cubic spline

Abstract

The goal of this work is to make a comparative analysis between the standard finite difference method and the non-standard finite difference method, then to make a non-standard discretization of the advection-diffusion-reaction equation with a reaction modelling a logistic growth which can be the evolution of the concentration of a microbial population in a medium, the equation will thus model transport and diffusion of this population in the aforementioned medium in one dimension of space and one makes numerical simulations to compare the non-standard scheme and the Euler’s scheme, explicit in time, implicit for the first order derivative in  and centered for the second order derivative in . One arrives by constructing a scheme of the advection-reaction equation, then adds the term of diffusion to obtain the non-standard scheme.

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Published

2022-04-02

How to Cite

Fotso Fotso, G. P., Balkissou Hamidou, & Achille Landri Pokam Kakeu. (2022). Non-Standard Discretization of the Advection-Diffusion-Reaction Equation with Logistic Growth Reaction. International Journal of Computer (IJC), 42(1), 59–90. Retrieved from https://ijcjournal.org/index.php/InternationalJournalOfComputer/article/view/1917

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