Stability And Convergence Analysis Of The High-accuracy Numerical Algorithm For Fractional Cable Equation

Fractional diferential equations have been widely applied in the field of scienceand engineering. For example, the fractional cable equation has become one ofthe most important equations to simulate neural dynamics. Therefore, it is verysignificant to study the numerical methods and relevant theory of the fractionalcable equation.This paper constructs a high-accuracy algorithm for solving fractional cableequation by the method in the reference documentation. The stability and conver-gence of the high-accuracy numerical method are analyzed by Fourier analysis. Andthe numerical method is convergent of the order (1++4). Finally, the resultsof numerical examples support the theoretical analysis.