The design of new high-order group iterative method in the solution of two-dimensional fractional cable equation

• Main Authors: Muhammad Asim Khan, Norhashidah Hj. Mohd Ali, Nur Nadiah Abd Hamid
• Format: Article
• Language: English
• Published: Elsevier 2021-08-01
• Series: Alexandria Engineering Journal
• Subjects: Two-dimensional fractional cable equation; High-order finite difference method; Explicit group method; Crank Nicolson; Stability and convergence
• Online Access: http://www.sciencedirect.com/science/article/pii/S1110016821000119

In this article, a new high-order explicit group iterative scheme is developed for the solution of the two-dimensional time fractional cable equation. The proposed scheme is derived from the Crank-Nicolson (C-N) high-order compact finite difference method, where the Caputo discretization and C-N high-order approximations are used for the time fractional and space derivative respectively. The stability and convergence of the proposed scheme are also established. Finally, two numerical examples are presented to show the accuracy and efficiency of the scheme.