A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation.

Abstract

In this article, we developed a new higher-order implicit finite difference iterative scheme (FDIS) for the solution of the two dimension (2-D) time fractional Cable equation (FCE). In the new proposed FDIS, the time fractional and space derivatives are discretized using the Caputo fractional derivative and fourth-order implicit scheme, respectively. Moreover, the proposed scheme theoretical analysis (convergence and stability) is also discussed using the Fourier analysis method. Finally, some numerical test problems are presented to show the effectiveness of the proposed method.