A robust numerical method based on Jaiswal–Laguerre functions for the classical FitzHugh–Nagumo model

Purpose This paper aims to address the generalized FitzHugh–Nagumo equation by introducing an effective numerical method based on Jaiswal–Laguerre functions. Design/methodology/approach This paper uses pseudo-operational matrices and a collocation method to numerically solve the generalized FitzHugh–Nagumo problem. Using the Jaiswal–Laguerre functions to approximate the solution, the problem is converted into an algebraic system of equations. Findings We analyze the error bounds of the approximation functions in detail to confirm theoretical accuracy. Several numerical simulations are carried out to confirm the accuracy, robustness and computing efficiency of the proposed method. Research limitations/implications Despite the method's high accuracy and robustness, the effectiveness of the proposed numerical approach depends on the selection of Jaiswal–Laguerre parameters, which may need to be modified for specific problem conditions. Additionally, the approach has only been tested in a limited number of numerical experiments, and more investigation is required to see whether it can be used for higher-dimensional or more sophisticated variants of the FitzHugh–Nagumo problem. Originality/value Numerical simulations are performed on four different scenarios to confirm the theoretical findings. The superiority of the proposed approach over other existing schemes in the literature is shown by comparing the associated maximum absolute errors.