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Finite element analysis of nonlinear reaction–diffusion system of Fitzhugh–Nagumo type with Robin boundary conditions

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  • Al-Juaifri, Ghassan A.
  • Harfash, Akil J.

Abstract

In this paper, we investigate the numerical analysis of Fitzhugh–Nagumo (FHN) reaction–diffusion equations. The properties of numerical solutions of a semi-discrete and fully-practical piecewise linear finite element technique are provided. Moreover, for a semi-discrete and fully discrete finite element approximation, we establish a priori estimates and error bounds. We also introduce the results of some numerical examples in one and two dimensions, which confirm the theoretical findings of this paper.

Suggested Citation

  • Al-Juaifri, Ghassan A. & Harfash, Akil J., 2023. "Finite element analysis of nonlinear reaction–diffusion system of Fitzhugh–Nagumo type with Robin boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 486-517.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:486-517
    DOI: 10.1016/j.matcom.2022.07.005
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    Cited by:

    1. Mufutau Ajani Rufai & Athinoula A. Kosti & Zacharias A. Anastassi & Bruno Carpentieri, 2023. "A New Two-Step Hybrid Block Method for the FitzHugh–Nagumo Model Equation," Mathematics, MDPI, vol. 12(1), pages 1-13, December.

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