The Innovation Iterative Method and its Stability in Time-Fractional Diffusion Equations
In this research, we deal with the innovation or application iterative methods of an unconditionally implicit finite difference approximation equation and the one-dimensional, linear time fractional diffusion equations (TFDEs) via Caputo’s time fractional derivative. Based on this implicit approxima...
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| Format: | Article |
| Language: | English English |
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2020
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| Online Access: | https://eprints.ums.edu.my/id/eprint/26177/1/The%20Innovation%20Iterative%20Method%20and%20its%20Stability%20in%20Time-Fractional%20Diffusion%20Equations.pdf https://eprints.ums.edu.my/id/eprint/26177/2/The%20Innovation%20Iterative%20Method%20and%20its%20Stability%20in%20Time-Fractional%20Diffusion%20Equations1.pdf |
| _version_ | 1825713980724740096 |
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| author | Andang Sunarto Jumat Sulaiman |
| author_facet | Andang Sunarto Jumat Sulaiman |
| author_sort | Andang Sunarto |
| collection | UMS |
| description | In this research, we deal with the innovation or application iterative methods of an unconditionally implicit finite difference approximation equation and the one-dimensional, linear time fractional diffusion equations (TFDEs) via Caputo’s time fractional derivative. Based on this implicit approximation equation, the corresponding linear system can be generated, in which its coefficient matrix is large scale and sparse. To speed up the convergence rate in solving the linear system iteratively, we construct the corresponding preconditioned linear system. Then we formulate and implement the Preconditioned Gauss-Seidel (PGS) iterative method for solving the generated linear system. Two examples of the problem are presented to illustrate the effectiveness of the PGS method. The two numerical results of this study show that the proposed iterative method is superior to the basic GS iterative method. |
| first_indexed | 2024-03-06T03:04:58Z |
| format | Article |
| id | ums.eprints-26177 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:04:58Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ums.eprints-261772021-01-15T08:03:12Z https://eprints.ums.edu.my/id/eprint/26177/ The Innovation Iterative Method and its Stability in Time-Fractional Diffusion Equations Andang Sunarto Jumat Sulaiman Q Science (General) In this research, we deal with the innovation or application iterative methods of an unconditionally implicit finite difference approximation equation and the one-dimensional, linear time fractional diffusion equations (TFDEs) via Caputo’s time fractional derivative. Based on this implicit approximation equation, the corresponding linear system can be generated, in which its coefficient matrix is large scale and sparse. To speed up the convergence rate in solving the linear system iteratively, we construct the corresponding preconditioned linear system. Then we formulate and implement the Preconditioned Gauss-Seidel (PGS) iterative method for solving the generated linear system. Two examples of the problem are presented to illustrate the effectiveness of the PGS method. The two numerical results of this study show that the proposed iterative method is superior to the basic GS iterative method. 2020 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/26177/1/The%20Innovation%20Iterative%20Method%20and%20its%20Stability%20in%20Time-Fractional%20Diffusion%20Equations.pdf text en https://eprints.ums.edu.my/id/eprint/26177/2/The%20Innovation%20Iterative%20Method%20and%20its%20Stability%20in%20Time-Fractional%20Diffusion%20Equations1.pdf Andang Sunarto and Jumat Sulaiman (2020) The Innovation Iterative Method and its Stability in Time-Fractional Diffusion Equations. International Journal of Innovation, Creativity and Change. pp. 560-579. |
| spellingShingle | Q Science (General) Andang Sunarto Jumat Sulaiman The Innovation Iterative Method and its Stability in Time-Fractional Diffusion Equations |
| title | The Innovation Iterative Method and its Stability in Time-Fractional Diffusion Equations |
| title_full | The Innovation Iterative Method and its Stability in Time-Fractional Diffusion Equations |
| title_fullStr | The Innovation Iterative Method and its Stability in Time-Fractional Diffusion Equations |
| title_full_unstemmed | The Innovation Iterative Method and its Stability in Time-Fractional Diffusion Equations |
| title_short | The Innovation Iterative Method and its Stability in Time-Fractional Diffusion Equations |
| title_sort | innovation iterative method and its stability in time fractional diffusion equations |
| topic | Q Science (General) |
| url | https://eprints.ums.edu.my/id/eprint/26177/1/The%20Innovation%20Iterative%20Method%20and%20its%20Stability%20in%20Time-Fractional%20Diffusion%20Equations.pdf https://eprints.ums.edu.my/id/eprint/26177/2/The%20Innovation%20Iterative%20Method%20and%20its%20Stability%20in%20Time-Fractional%20Diffusion%20Equations1.pdf |
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