Numerical Investigation on the Solution of a Space-Fractional via Preconditioned SOR Iterative Method
This paper considers a numerical investigation on the solution of a one-dimensional linear space-fractional partial differential equation with the application of an unconditionally implicit finite difference method and the Caputo’s space-fractional derivative. We formulate the Caputo’simplicit finit...
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| Format: | Article |
| Language: | English English |
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Natural Sciences Publishing Cor.
2022
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| Online Access: | https://eprints.ums.edu.my/id/eprint/33807/1/Numerical%20Investigation%20on%20the%20Solution%20of%20a%20Space-Fractional%20via%20Preconditioned%20SOR%20Iterative%20Method.pdf https://eprints.ums.edu.my/id/eprint/33807/2/Numerical%20Investigation%20on%20the%20Solution%20of%20a%20Space-Fractional%20via%20Preconditioned%20SOR%20Iterative%20Method1.pdf |
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| author | Andang Sunarto Praveen Agarwal Jumat Sulaiman Chew, Jackel Vui Lung |
| author_facet | Andang Sunarto Praveen Agarwal Jumat Sulaiman Chew, Jackel Vui Lung |
| author_sort | Andang Sunarto |
| collection | UMS |
| description | This paper considers a numerical investigation on the solution of a one-dimensional linear space-fractional partial differential equation with the application of an unconditionally implicit finite difference method and the Caputo’s space-fractional derivative. We formulate the Caputo’simplicit finite difference approximation equation to form a corresponding linear system in which its coefficient matrix is large-sized and has a great sparsity. We construct a preconditioned linear system intending to speed up the convergence rate in computing the solutions of the linear system using the SOR iterative method. We present two examples of the one-dimensional linear space-fractional partial differential equation problem to illustrate the effectiveness and efficiency of our proposed PSOR iterative method. Through the investigation, the numerical results show that the proposed PSOR iterative method is superior to the preconditioned Gauss-Seidel and Gauss-Seidel iterative methods in terms of efficiency. |
| first_indexed | 2024-03-06T03:19:15Z |
| format | Article |
| id | ums.eprints-33807 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:19:15Z |
| publishDate | 2022 |
| publisher | Natural Sciences Publishing Cor. |
| record_format | dspace |
| spelling | ums.eprints-338072022-08-16T07:31:54Z https://eprints.ums.edu.my/id/eprint/33807/ Numerical Investigation on the Solution of a Space-Fractional via Preconditioned SOR Iterative Method Andang Sunarto Praveen Agarwal Jumat Sulaiman Chew, Jackel Vui Lung Q1-390 Science (General) QA1-939 Mathematics This paper considers a numerical investigation on the solution of a one-dimensional linear space-fractional partial differential equation with the application of an unconditionally implicit finite difference method and the Caputo’s space-fractional derivative. We formulate the Caputo’simplicit finite difference approximation equation to form a corresponding linear system in which its coefficient matrix is large-sized and has a great sparsity. We construct a preconditioned linear system intending to speed up the convergence rate in computing the solutions of the linear system using the SOR iterative method. We present two examples of the one-dimensional linear space-fractional partial differential equation problem to illustrate the effectiveness and efficiency of our proposed PSOR iterative method. Through the investigation, the numerical results show that the proposed PSOR iterative method is superior to the preconditioned Gauss-Seidel and Gauss-Seidel iterative methods in terms of efficiency. Natural Sciences Publishing Cor. 2022 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/33807/1/Numerical%20Investigation%20on%20the%20Solution%20of%20a%20Space-Fractional%20via%20Preconditioned%20SOR%20Iterative%20Method.pdf text en https://eprints.ums.edu.my/id/eprint/33807/2/Numerical%20Investigation%20on%20the%20Solution%20of%20a%20Space-Fractional%20via%20Preconditioned%20SOR%20Iterative%20Method1.pdf Andang Sunarto and Praveen Agarwal and Jumat Sulaiman and Chew, Jackel Vui Lung (2022) Numerical Investigation on the Solution of a Space-Fractional via Preconditioned SOR Iterative Method. Progress in Fractional Differentiation and Applications An International Journal, 8 (2). pp. 289-295. ISSN 2356-9336 (P-ISSN) , 2356-9344 (E-ISSN) https://www.naturalspublishing.com/files/published/8w4zcy2u73d442.pdf http://dx.doi.org/10.18576/pfda/080208 http://dx.doi.org/10.18576/pfda/080208 |
| spellingShingle | Q1-390 Science (General) QA1-939 Mathematics Andang Sunarto Praveen Agarwal Jumat Sulaiman Chew, Jackel Vui Lung Numerical Investigation on the Solution of a Space-Fractional via Preconditioned SOR Iterative Method |
| title | Numerical Investigation on the Solution of a Space-Fractional via Preconditioned SOR Iterative Method |
| title_full | Numerical Investigation on the Solution of a Space-Fractional via Preconditioned SOR Iterative Method |
| title_fullStr | Numerical Investigation on the Solution of a Space-Fractional via Preconditioned SOR Iterative Method |
| title_full_unstemmed | Numerical Investigation on the Solution of a Space-Fractional via Preconditioned SOR Iterative Method |
| title_short | Numerical Investigation on the Solution of a Space-Fractional via Preconditioned SOR Iterative Method |
| title_sort | numerical investigation on the solution of a space fractional via preconditioned sor iterative method |
| topic | Q1-390 Science (General) QA1-939 Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/33807/1/Numerical%20Investigation%20on%20the%20Solution%20of%20a%20Space-Fractional%20via%20Preconditioned%20SOR%20Iterative%20Method.pdf https://eprints.ums.edu.my/id/eprint/33807/2/Numerical%20Investigation%20on%20the%20Solution%20of%20a%20Space-Fractional%20via%20Preconditioned%20SOR%20Iterative%20Method1.pdf |
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