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

Khan MA 1 , Alias N 2 , Khan I 3 , Salama FM 4 , Eldin SM 5

Affiliations 

  • 1 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia. [email protected]
  • 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. [email protected]
  • 5 Center of Research, Faculty of Engineering, Future University in Egypt, 11835, New Cairo, Egypt
Sci Rep, 2023 Jan 27;13(1):1549.
PMID: 36707653 DOI: 10.1038/s41598-023-28741-7

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.

* Title and MeSH Headings from MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine.

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