Andang Sunarto, Andang (2021) Computational Approach via HalfSweep and Preconditioned AOR for Fractional Diffusion. Intelligent Automation & Soft Computing, 31 (2). ISSN 2326005X

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Abstract
Solving timefractional diffusion equation using a numerical method has become a research trend nowadays since analytical approaches are quite limited. There is increasing usage of the finite difference method, but the efficiency of the scheme still needs to be explored. A halfsweep finite difference scheme is wellknown as a computational complexity reduction approach. Therefore, the present paper applied an unconditionally stable halfsweep finite difference scheme to solve the timefractional diffusion equation in a onedimensional model. Throughout this paper, a Caputo fractional operator is used to substitute the timefractional derivative term approximately. Then, the stability of the difference scheme combining the halfsweep finite difference for spatial discretization and Caputo timefractional derivative is analyzed for its compatibility. From the formulated halfsweep Caputo approximation to the timefractional diffusion equation, a linear system corresponds to the equation contains a large and sparse coefficient matrix that needs to be solved efficiently. We construct a preconditioned matrix based on the first matrix and develop a preconditioned accelerated over relaxation (PAOR) algorithm to achieve a high convergence solution. The convergence of the developed method is analyzed. Finally, some numerical experiments from our research are given to illustrate the efficiency of our computational approach to solve the proposed problems of timefractional diffusion. The combination of a halfsweep finite difference scheme and PAOR algorithm can be a good alternative computational approach to solve the timefractional diffusion equationbased mathematical physics model.
Item Type:  Article 

Uncontrolled Keywords:  Timefractional diffusion; halfsweep; finite difference discretization method; preconditioned accelerated over relaxation algorithm 
Subjects:  Q Science > QA Mathematics 
Depositing User:  S.IP Muhammad Yusrizal 
Date Deposited:  23 Sep 2021 03:58 
Last Modified:  23 Sep 2021 03:58 
URI:  http://repository.iainbengkulu.ac.id/id/eprint/7089 
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