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An innovative approach to modeling the conduction of electrical impulses via intricate neuronal structures is introduced in this paper, which offers a theoretical and computational examination of parameter estimation in a coupled FitzHugh–Nagumo model. With this goal in mind, we present a finite volume approach to solving the FitzHugh–Nagumo model and check the numerical method's accuracy against previous findings. To further assess and contrast the efficacy and precision of the model's outputs, a finite difference formulation is incorporated. To clarify the basic qualitative properties of the inhibitor–activator mechanism intrinsic to the coupled FitzHugh–Nagumo model, the analysis uses dynamical system approaches and linear stability analysis. The results show that the suggested schemes are very accurate, with conditional stability, reaching fourth-order spatial and second-order temporal precision. The results are given in both tabular and graphical forms. According to numerical results, the suggested finite volume method outperforms the finite difference method in accurately and efficiently solving the nonlinear coupled FitzHugh–Nagumo model. Neuronal activity and electrical communication are complex biological systems with a lot of investigated nonlinear differential equations; this research helps us understand more about these topics. [ABSTRACT FROM AUTHOR]