Mixed two‐grid finite difference methods for solving one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations

Abstract

The aim of this paper is to propose mixed two‐grid finite difference methods to obtain the numerical solution of the one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations. The finite difference equations at all interior grid points form a large‐sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The proposed method is based on applying a family of finite difference methods for discretizing the spatial and time derivatives. The obtained system has been solved by two‐grid method, where the two‐grid method is used for solving the large‐sparse linear systems. Also, in the proposed method, the spectral radius with local Fourier analysis is calculated for different values of h and Δt. The numerical examples show the efficiency of this algorithm for solving the one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations. Copyright © 2016 John Wiley & Sons, Ltd.

Efficient numerical method for the Fitzhugh-Nagumo equations with Neumann boundary conditions

“…In the past few decades, many researchers have done for the numerical solution of the FN equations. Various numerical methods have been announced including the finite difference method [4][5][6], Haar wavelet method [7], finite element method [8][9], spectral method [2,[10][11][12] and so on [3]. Recently, Muhammad et al derived a stochastic explicit scheme to approximate the stochastic FN model.…”