New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation
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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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ISRP Style
Ajmal Ali, Muhammad Abbas, Tayyaba Akram, New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation, Journal of Mathematics and Computer Science, 22 (2021), no. 2, 119--127
AMA Style
Ali Ajmal, Abbas Muhammad, Akram Tayyaba, New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation. J Math Comput SCI-JM. (2021); 22(2):119--127
Chicago/Turabian Style
Ali, Ajmal, Abbas, Muhammad, Akram, Tayyaba. "New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation." Journal of Mathematics and Computer Science, 22, no. 2 (2021): 119--127
Keywords
- Riemann-Liouville fractional derivative
- fractional implicit standard point
- fractional implicit rotated point
- anomalous fractional sub-diffusion equation
MSC
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