New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation

© 2022 The Author(s)The present paper investigates the approximate solution of a one-dimensional linear space-fractional diffusion equation using a new preconditioning matrix to develop an efficient half-sweep accelerated overrelaxation iterative method. The proposed method utilizes unconditionally...

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Main Authors: Praveen Agarwal, Andang Sunarto, Jackel Vui Lung Chew, Jumat Sulaiman, Shaher Momani
Format: Article
Language:English
English
Published: ResearchGate 2023
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Online Access:https://eprints.ums.edu.my/id/eprint/36037/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/36037/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/36037/
https://doi.org/10.1016/j.jksus.2022.102461
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Institution: Universiti Malaysia Sabah
Language: English
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spelling my.ums.eprints.360372023-09-01T00:46:38Z https://eprints.ums.edu.my/id/eprint/36037/ New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation Praveen Agarwal Andang Sunarto Jackel Vui Lung Chew Jumat Sulaiman Shaher Momani QA1-939 Mathematics QA299.6-433 Analysis © 2022 The Author(s)The present paper investigates the approximate solution of a one-dimensional linear space-fractional diffusion equation using a new preconditioning matrix to develop an efficient half-sweep 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 space-fractional 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, half-sweep preconditioned accelerated overrelaxation, has the potential to solve a variety of space-fractional diffusion models efficiently. Future investigation will improve the absolute errors of the solutions. ResearchGate 2023-02 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/36037/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/36037/2/FULL%20TEXT.pdf Praveen Agarwal and Andang Sunarto and Jackel Vui Lung Chew and Jumat Sulaiman and Shaher Momani (2023) New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation. Journal of King Saud University - Science, 35. pp. 1-10. ISSN 1018-3647 https://doi.org/10.1016/j.jksus.2022.102461
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
English
topic QA1-939 Mathematics
QA299.6-433 Analysis
spellingShingle QA1-939 Mathematics
QA299.6-433 Analysis
Praveen Agarwal
Andang Sunarto
Jackel Vui Lung Chew
Jumat Sulaiman
Shaher Momani
New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation
description © 2022 The Author(s)The present paper investigates the approximate solution of a one-dimensional linear space-fractional diffusion equation using a new preconditioning matrix to develop an efficient half-sweep 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 space-fractional 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, half-sweep preconditioned accelerated overrelaxation, has the potential to solve a variety of space-fractional diffusion models efficiently. Future investigation will improve the absolute errors of the solutions.
format Article
author Praveen Agarwal
Andang Sunarto
Jackel Vui Lung Chew
Jumat Sulaiman
Shaher Momani
author_facet Praveen Agarwal
Andang Sunarto
Jackel Vui Lung Chew
Jumat Sulaiman
Shaher Momani
author_sort Praveen Agarwal
title New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation
title_short New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation
title_full New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation
title_fullStr New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation
title_full_unstemmed New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation
title_sort new preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation
publisher ResearchGate
publishDate 2023
url https://eprints.ums.edu.my/id/eprint/36037/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/36037/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/36037/
https://doi.org/10.1016/j.jksus.2022.102461
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