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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| Format: | Article |
| Language: | English English |
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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 |
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| 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 |
| collection | UMS |
| 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. |
| first_indexed | 2024-03-06T03:24:14Z |
| format | Article |
| id | ums.eprints-36037 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:24:14Z |
| publishDate | 2023 |
| publisher | ResearchGate |
| record_format | dspace |
| spelling | 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 |
| 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 |
| title | 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_short | 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 |
| topic | QA1-939 Mathematics QA299.6-433 Analysis |
| url | https://eprints.ums.edu.my/id/eprint/36037/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/36037/2/FULL%20TEXT.pdf |
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