Praveen Agarwal and Andang Sunarto and Jackel Vui Lung Chew and Jumat Sulaiman and Shaher Momani (2023) New preconditioning and halfsweep accelerated overrelaxation solution for fractional differential equation. Journal of King Saud University  Science, 35. pp. 110. ISSN 10183647
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Abstract
© 2022 The Author(s)The present paper investigates the approximate solution of a onedimensional linear spacefractional diffusion equation using a new preconditioning matrix to develop an efficient halfsweep accelerated overrelaxation iterative method. The proposed method utilizes unconditionally stable implicit finite difference schemes to formulate the discrete approximation equation to the problem. The formulation employs the Caputo fractional derivative to treat the spacefractional derivative in the problem. The paper's focus is to assess the improvement in terms of the convergence rate of the solution obtained by the proposed iterative method. The numerical experiment illustrates the superiority of the proposed method in terms of solution efficiency against one of the existing preconditioned methods, preconditioned accelerated overrelaxation and implicit Euler method. The proposed method reveals the ability to compute the solution with lesser iterations and faster computation time than the preconditioned accelerated overrelaxation and implicit Euler method. The method introduced in the paper, halfsweep preconditioned accelerated overrelaxation, has the potential to solve a variety of spacefractional diffusion models efficiently. Future investigation will improve the absolute errors of the solutions.
Item Type:  Article 

Keyword:  Accelerated overrelaxation;Caputo fractional derivative;Finite difference method;Halfsweep;Preconditioning matrix;Spacefractional derivative; 
Subjects:  Q Science > QA Mathematics > QA1939 Mathematics Q Science > QA Mathematics > QA1939 Mathematics > QA299.6433 Analysis 
Department:  FACULTY > Faculty of Computing and Informatics FACULTY > Faculty of Science and Natural Resources 
Depositing User:  ABDULLAH BIN SABUDIN  
Date Deposited:  01 Sep 2023 08:46 
Last Modified:  01 Sep 2023 08:46 
URI:  https://eprints.ums.edu.my/id/eprint/36037 
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