SOR method for the implicit finite difference solution of time-fractional diffusion equations
In this study, we derive an unconditionally implicit finite difference approximation equation from the discretization of the one-dimensional linear time fractional diffusion equations by using the Caputo’s time fractional derivative. Then this approximation equation hence will be used to generate th...
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| Format: | Article |
| Language: | English English |
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Universiti Malaysia Sabah
2014
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| Online Access: | https://eprints.ums.edu.my/id/eprint/20379/1/SOR%20method%20for%20the%20implicit%20finite%20difference%20solution%20of%20time.pdf https://eprints.ums.edu.my/id/eprint/20379/7/SOR%20method%20for%20the%20implicit%20finite%20difference%20solution%20of%20time-fractional%20diffusion%20equations.pdf |
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| author | A. Sunarto Jumat Sulaiman Azali Saudi |
| author_facet | A. Sunarto Jumat Sulaiman Azali Saudi |
| author_sort | A. Sunarto |
| collection | UMS |
| description | In this study, we derive an unconditionally implicit finite difference approximation equation from the discretization of the one-dimensional linear time fractional diffusion equations by using the Caputo’s time fractional derivative. Then this approximation equation hence will be used to generate the corresponding system of linear equations. The approximation solution of the linear system is described via the implementation of Successive Over-Relaxation (SOR) iterative method. An example of the problem is presented to illustrate the effectiveness of SOR method. The findings of this study show that the proposed iterative method is superior compared with the Gauss-Seidel iterative method. |
| first_indexed | 2024-03-06T02:57:41Z |
| format | Article |
| id | ums.eprints-20379 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T02:57:41Z |
| publishDate | 2014 |
| publisher | Universiti Malaysia Sabah |
| record_format | dspace |
| spelling | ums.eprints-203792021-01-11T08:59:08Z https://eprints.ums.edu.my/id/eprint/20379/ SOR method for the implicit finite difference solution of time-fractional diffusion equations A. Sunarto Jumat Sulaiman Azali Saudi TC Hydraulic engineering. Ocean engineering In this study, we derive an unconditionally implicit finite difference approximation equation from the discretization of the one-dimensional linear time fractional diffusion equations by using the Caputo’s time fractional derivative. Then this approximation equation hence will be used to generate the corresponding system of linear equations. The approximation solution of the linear system is described via the implementation of Successive Over-Relaxation (SOR) iterative method. An example of the problem is presented to illustrate the effectiveness of SOR method. The findings of this study show that the proposed iterative method is superior compared with the Gauss-Seidel iterative method. Universiti Malaysia Sabah 2014 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/20379/1/SOR%20method%20for%20the%20implicit%20finite%20difference%20solution%20of%20time.pdf text en https://eprints.ums.edu.my/id/eprint/20379/7/SOR%20method%20for%20the%20implicit%20finite%20difference%20solution%20of%20time-fractional%20diffusion%20equations.pdf A. Sunarto and Jumat Sulaiman and Azali Saudi (2014) SOR method for the implicit finite difference solution of time-fractional diffusion equations. Borneo Science, 34. ISSN 1394-4339 http://borneoscience.ums.edu.my/?p=1153 |
| spellingShingle | TC Hydraulic engineering. Ocean engineering A. Sunarto Jumat Sulaiman Azali Saudi SOR method for the implicit finite difference solution of time-fractional diffusion equations |
| title | SOR method for the implicit finite difference solution of time-fractional diffusion equations |
| title_full | SOR method for the implicit finite difference solution of time-fractional diffusion equations |
| title_fullStr | SOR method for the implicit finite difference solution of time-fractional diffusion equations |
| title_full_unstemmed | SOR method for the implicit finite difference solution of time-fractional diffusion equations |
| title_short | SOR method for the implicit finite difference solution of time-fractional diffusion equations |
| title_sort | sor method for the implicit finite difference solution of time fractional diffusion equations |
| topic | TC Hydraulic engineering. Ocean engineering |
| url | https://eprints.ums.edu.my/id/eprint/20379/1/SOR%20method%20for%20the%20implicit%20finite%20difference%20solution%20of%20time.pdf https://eprints.ums.edu.my/id/eprint/20379/7/SOR%20method%20for%20the%20implicit%20finite%20difference%20solution%20of%20time-fractional%20diffusion%20equations.pdf |
| work_keys_str_mv | AT asunarto sormethodfortheimplicitfinitedifferencesolutionoftimefractionaldiffusionequations AT jumatsulaiman sormethodfortheimplicitfinitedifferencesolutionoftimefractionaldiffusionequations AT azalisaudi sormethodfortheimplicitfinitedifferencesolutionoftimefractionaldiffusionequations |