A New Two-Step Hybrid Block Method for the FitzHugh–Nagumo Model Equation

Mufutau Ajani Rufai (), Athinoula A. Kosti, Zacharias A. Anastassi and Bruno Carpentieri
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Mufutau Ajani Rufai: Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, Italy
Athinoula A. Kosti: Institute of Artificial Intelligence, School of Computer Science and Informatics, De Montfort University, Leicester LE1 9BH, UK
Zacharias A. Anastassi: Institute of Artificial Intelligence, School of Computer Science and Informatics, De Montfort University, Leicester LE1 9BH, UK
Bruno Carpentieri: Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, Italy

Mathematics, 2023, vol. 12, issue 1, 1-13

Abstract: This paper presents an efficient two-step hybrid block method (ETHBM) to obtain an approximate solution to the FitzHugh–Nagumo problem. The considered partial differential equation model problems are semi-discretized, reducing them to equivalent ordinary differential equations using the method of lines. In order to evaluate the effectiveness of the proposed ETHBM, three numerical examples are presented and compared with the results obtained through existing methods. The results demonstrate that the proposed ETHBM produces more efficient results than some other numerical approaches in the literature.

Keywords: hybrid block method; partial differential equations; collocation method; FitzHugh–Nagumo equations; stability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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