Implicit finite difference solution for time-fractional diffusion equations using AOR method
In this paper, we derive an implicit finite difference approximation equation of the one-dimensional linear time fractional diffusion equations, based on the Caputo's time fractional derivative. Then this approximation equation leads the corresponding system of linear equation, which is large s...
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| Format: | Article |
| Language: | English English |
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Institute of Physics Publishing
2014
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| Online Access: | https://eprints.ums.edu.my/id/eprint/21449/1/Implicit%20finite%20difference%20solution%20for%20time-fractional%20diffusion%20equations%20using%20AOR%20method.pdf https://eprints.ums.edu.my/id/eprint/21449/7/Implicit%20finite%20difference%20solution%20for%20time-fractional%20diffusion%20equations%20using%20AOR%20method.pdf |
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| author | A. Sunarto Sulaiman J. Azali Saudi |
| author_facet | A. Sunarto Sulaiman J. Azali Saudi |
| author_sort | A. Sunarto |
| collection | UMS |
| description | In this paper, we derive an implicit finite difference approximation equation of the one-dimensional linear time fractional diffusion equations, based on the Caputo's time fractional derivative. Then this approximation equation leads the corresponding system of linear equation, which is large scale and sparse. Due to the characteristics of the coefficient matrix, we use the Accelerated Over-Relaxation (AOR) iterative method for solving the generated linear system. One example of the problem is presented to illustrate the effectiveness of AOR method. The numerical results of this study show that the proposed iterative method is superior compared with the existing one weighted parameter iterative method. |
| first_indexed | 2024-03-06T02:58:32Z |
| format | Article |
| id | ums.eprints-21449 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T02:58:32Z |
| publishDate | 2014 |
| publisher | Institute of Physics Publishing |
| record_format | dspace |
| spelling | ums.eprints-214492021-01-11T09:00:23Z https://eprints.ums.edu.my/id/eprint/21449/ Implicit finite difference solution for time-fractional diffusion equations using AOR method A. Sunarto Sulaiman J. Azali Saudi QA Mathematics In this paper, we derive an implicit finite difference approximation equation of the one-dimensional linear time fractional diffusion equations, based on the Caputo's time fractional derivative. Then this approximation equation leads the corresponding system of linear equation, which is large scale and sparse. Due to the characteristics of the coefficient matrix, we use the Accelerated Over-Relaxation (AOR) iterative method for solving the generated linear system. One example of the problem is presented to illustrate the effectiveness of AOR method. The numerical results of this study show that the proposed iterative method is superior compared with the existing one weighted parameter iterative method. Institute of Physics Publishing 2014 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/21449/1/Implicit%20finite%20difference%20solution%20for%20time-fractional%20diffusion%20equations%20using%20AOR%20method.pdf text en https://eprints.ums.edu.my/id/eprint/21449/7/Implicit%20finite%20difference%20solution%20for%20time-fractional%20diffusion%20equations%20using%20AOR%20method.pdf A. Sunarto and Sulaiman J. and Azali Saudi (2014) Implicit finite difference solution for time-fractional diffusion equations using AOR method. Journal of Physics: Conference Series (495). pp. 1-8. ISSN 1742-6596 https://doi:10.1088/1742-6596/495/1/012032 |
| spellingShingle | QA Mathematics A. Sunarto Sulaiman J. Azali Saudi Implicit finite difference solution for time-fractional diffusion equations using AOR method |
| title | Implicit finite difference solution for time-fractional diffusion equations using AOR method |
| title_full | Implicit finite difference solution for time-fractional diffusion equations using AOR method |
| title_fullStr | Implicit finite difference solution for time-fractional diffusion equations using AOR method |
| title_full_unstemmed | Implicit finite difference solution for time-fractional diffusion equations using AOR method |
| title_short | Implicit finite difference solution for time-fractional diffusion equations using AOR method |
| title_sort | implicit finite difference solution for time fractional diffusion equations using aor method |
| topic | QA Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/21449/1/Implicit%20finite%20difference%20solution%20for%20time-fractional%20diffusion%20equations%20using%20AOR%20method.pdf https://eprints.ums.edu.my/id/eprint/21449/7/Implicit%20finite%20difference%20solution%20for%20time-fractional%20diffusion%20equations%20using%20AOR%20method.pdf |
| work_keys_str_mv | AT asunarto implicitfinitedifferencesolutionfortimefractionaldiffusionequationsusingaormethod AT sulaimanj implicitfinitedifferencesolutionfortimefractionaldiffusionequationsusingaormethod AT azalisaudi implicitfinitedifferencesolutionfortimefractionaldiffusionequationsusingaormethod |