Stability and convergence analysis of Fourier pseudo-spectral method for FitzHugh-Nagumo model (Q2192644)

This article discusses the stability and convergence of the Fourier pseudo-spectral scheme coupled with several linearized finite difference methods for the FitzHugh-Nagumo model. The approach relies on the use of the first- and second-order scheme for time discretization and Fourier pseudo-spectral method for spatial discretization. By constructing an auxiliary interpolation equation, the authors obtain \(L^\infty\) uniform boundedness and error estimates of the numerical solutions. Numerical experiments are included to support the theoretical findings.