Barycentric–Legendre Interpolation Method for Solving Two-Dimensional Fractional Cable Equation in Neuronal Dynamics

This paper presents a spectral collocation method with the goal of estimating the solution of fractional cable equation in neuronal dynamics. The proposed method consists of expanding the unknown solution as the elements of the Barycentric basis and the shifted Legendre polynomials. The spatial derivative and time derivative are discretized using the Barycentric interpolation method and the Legendre polynomials, respectively. The differentiation matrix of the Barycentric method and the operational matrix of the Legendre polynomials are introduced. These matrices and the collocation points are applied to reduce the problem into a linear algebraic system. Eventually, some experimental examples are given to illustrate the efficiency and applicability of the method.