Numerical Simulation of Fitzhugh-Nagumo Dynamics Using a Finite Difference-Based Method of Lines

Abstract

This study investigates the numerical solution of the FitzHugh-Nagumo (FHN) equation, a canonical Nonlinear Reaction-Diffusion system widely used in Neuroscience and Biophysics using the Method of Lines (MoL). The MoL approach, known for its efficiency and flexibility, discretizes spatial variables to transform partial differential equations ( PDEs ) into a system of Ordinary Differential Equations (ODEs), which are then integrated in time. A fourth-order five-point central difference scheme is employed to approximate spatial derivatives, and MATLAB is used to implement the method. To validate the Numerical scheme, the Newell-Whitehead equation (a special case of the FHN model) is solved, and the results are benchmarked against exact solutions. The results exhibit excellent accuracy, with errors remaining in the order of 10−7 to 10−4 across varying time steps. Comparative analysis against results from the Galerkin Finite Element Method confirms the superior accuracy and computational efficiency of the MoL approach. These findings affirm the reliability and robustness of the Method of Lines in solving Nonlinear Reaction-Diffusion systems, suggesting its potential for broader application in modeling complex Scientific and Engineering phenomena.