Eur. Phys. J. Plus (2019) 134: 323
https://doi.org/10.1140/epjp/i2019-12730-y

Regular Article

A novel numerical method for solving the 2-D time fractional cable equation

¹ Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
² Department of Mathematics, Faculty of Education, Sana’a University, Sana’a, Yemen

^* e-mail: nsweilam@sci.cu.edu.eg

Received: 20 March 2019
Accepted: 24 April 2019
Published online: 10 July 2019

Abstract

In this paper, an efficient numerical scheme is constructed to approximate the solutions of the two-dimensional linear and nonlinear fractional cable equation. The fractional derivative is defined in the Atangana-Baleanu-Caputo sense. The nonstandard implicit compact finite difference method is presented to solve numerically the proposed equation. Special attention is given to studying the stability analysis of the numerical technique. Moreover, the truncation error is analyzed. Finally, two numerical test examples and comparative studies are presented. The numerical experiments demonstrate the high accuracy of the new method.