Second-order time integrators with the Fourier spectral method in application to multidimensional space-fractional FitzHugh-Nagumo model

Abstract

This paper investigated the propagation and interaction behavior of the fractional-in-space multidimensional FitzHugh-Nagumo model using second-order time integrators in combination with the Fourier spectral method. The study focused on analyzing the accuracy, efficiency and stability of these time integrators by comparing numerical results. The experimental findings highlight the ease of implementation and suitability of the methods for long-time simulations. Furthermore, the method's capability to capture the influence of the fractional operator on the equation's dynamics was examined.

Keywords

• fourier spectral method
• second-order time integrators
• space-fractional reaction-diffusion systems
• excitable systems
• fitzhugh-nagumo model