New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation

Volume 22, Issue 2, pp 119--127 http://dx.doi.org/10.22436/jmcs.022.02.03

Publication Date: July 16, 2020 Submission Date: March 31, 2020 Revision Date: April 23, 2020 Accteptance Date: May 24, 2020

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Authors

Ajmal Ali - Department of Mathematics, Virtual University of Pakistan, Lahore, Pakistan. Muhammad Abbas - Departemnt of Mathematics, University of Sargodha, Sargodha, Pakistan. Tayyaba Akram - School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia.

Abstract

In this paper, new group iterative schemes are developed for the numerical solution of two-dimensional anomalous fractional sub-diffusion equation subject to specific initial and Dirichlet boundary conditions. The new group relaxation iterative schemes are derived from the combination of standard and rotated (skewed) five-point modified implicit finite difference approximations. The results derived from the conducted numerical experiments show that fractional explicit de-coupled group (FEDG) iterative method has a significantly less computational cost in terms of CPU-timings as compared to the other iterative schemes, without threatening compromising accuracies.

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Keywords

• Riemann-Liouville fractional derivative
• fractional implicit standard point
• fractional implicit rotated point
• anomalous fractional sub-diffusion equation

MSC

•  65N06
•  65M06
•  65M12

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