High Accuracy Numerical Method For The Fractional Cable Equation

Fractional cable equation describes the movement of ion diffusion in the cell,it has become one of the most important equations to analog neural dynam-ics.In this paper,a high-accuracy numerical method for solving fractional cable equation is proposed in combination with the improved Griinwald-Letnikov method in the reference documentation and the compact finite difference. When the ratio of the grid satisfies certain conditions,the stability and convergence of the numerical method are analyzed by Fourier analysis, and the method is con-vergent of the order O(τ1+γmin+h4).Finally,the results of numerical examples support the theoretical analysis.