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

In this work, we discuss the stability and convergence of the Fourier pseudo-spectral scheme coupled with several linearized finite difference methods for FitzHugh-Nagumo model. The work of this article has three main features. Firstly, our full-discrete schemes are linear and easy to implement for two dimensional or three dimensional simulations. Secondly, by constructing the auxiliary interpolation equation, the L∞ uniform boundedness and the error estimate of the numerical solutions are obtained. Finally, the most important is that our numerical schemes are stable provided only time and space steps are bounded by two constants respectively. It is worth mentioning that this kind of stability restriction is very weak, it does not require any scaling law between time step and space size. Numerical examples are presented to verify validity of the proposed scheme.