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

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