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

Muhammad Asim Khan; Norma Alias; Ilyas Khan; Fouad Mohammad Salama; Sayed M Eldin

doi:10.1038/s41598-023-28741-7

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

Sci Rep. 2023 Jan 27;13(1):1549. doi: 10.1038/s41598-023-28741-7.

Authors

Muhammad Asim Khan¹, Norma Alias², Ilyas Khan³, Fouad Mohammad Salama⁴, Sayed M Eldin⁵

Affiliations

¹ Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia. asim.afg@gmail.com.
² Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia.
³ Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
⁴ Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. fuadmohd321@gmail.com.
⁵ Center of Research, Faculty of Engineering, Future University in Egypt, 11835, New Cairo, Egypt.

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.