Numerical Solution of the Time-fractional Diffusion Equations via Quarter-sweep Preconditioned Gauss-seidel Method
In this research, we propose the approximate solution of the time-fractional diffusion equation based on a quarter-sweep implicit finite difference approximation equation. To derive this approximation equation, Caputo's time-fractional derivative has been used to discretize the proposed problem...
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| Format: | Article |
| Language: | English English |
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Academic Publications
2021
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| Online Access: | https://eprints.ums.edu.my/id/eprint/32582/1/Numerical%20Solution%20of%20the%20Time-fractional%20Diffusion%20Equations%20via%20Quarter-sweep%20Preconditioned%20Gauss-seidel%20Method.pdf https://eprints.ums.edu.my/id/eprint/32582/3/Numerical%20Solution%20of%20the%20Time-fractional%20Diffusion%20Equations%20via%20Quarter-sweep%20Preconditioned%20Gauss-seidel%20Method%20_ABSTRACT.pdf |
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| author | Andang Sunarto Jumat Sulaiman Chew, Jackel Vui Lung |
| author_facet | Andang Sunarto Jumat Sulaiman Chew, Jackel Vui Lung |
| author_sort | Andang Sunarto |
| collection | UMS |
| description | In this research, we propose the approximate solution of the time-fractional diffusion equation based on a quarter-sweep implicit finite difference approximation equation. To derive this approximation equation, Caputo's time-fractional derivative has been used to discretize the proposed problems. By using the Caputo finite difference approximation equation, a linear system will be generated and solved iteratively. In addition to that, formulation and implementation the QSPGS iterative method are also presented. Based on the numerical results of the proposed iterative method, it can be concluded that the proposed iterative method is superior to the FSPGS and HSPGS iterative method. |
| first_indexed | 2024-03-06T03:15:58Z |
| format | Article |
| id | ums.eprints-32582 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:15:58Z |
| publishDate | 2021 |
| publisher | Academic Publications |
| record_format | dspace |
| spelling | ums.eprints-325822022-05-18T04:20:54Z https://eprints.ums.edu.my/id/eprint/32582/ Numerical Solution of the Time-fractional Diffusion Equations via Quarter-sweep Preconditioned Gauss-seidel Method Andang Sunarto Jumat Sulaiman Chew, Jackel Vui Lung QA1-939 Mathematics In this research, we propose the approximate solution of the time-fractional diffusion equation based on a quarter-sweep implicit finite difference approximation equation. To derive this approximation equation, Caputo's time-fractional derivative has been used to discretize the proposed problems. By using the Caputo finite difference approximation equation, a linear system will be generated and solved iteratively. In addition to that, formulation and implementation the QSPGS iterative method are also presented. Based on the numerical results of the proposed iterative method, it can be concluded that the proposed iterative method is superior to the FSPGS and HSPGS iterative method. Academic Publications 2021 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/32582/1/Numerical%20Solution%20of%20the%20Time-fractional%20Diffusion%20Equations%20via%20Quarter-sweep%20Preconditioned%20Gauss-seidel%20Method.pdf text en https://eprints.ums.edu.my/id/eprint/32582/3/Numerical%20Solution%20of%20the%20Time-fractional%20Diffusion%20Equations%20via%20Quarter-sweep%20Preconditioned%20Gauss-seidel%20Method%20_ABSTRACT.pdf Andang Sunarto and Jumat Sulaiman and Chew, Jackel Vui Lung (2021) Numerical Solution of the Time-fractional Diffusion Equations via Quarter-sweep Preconditioned Gauss-seidel Method. International Journal of Applied Mathematics, 34. pp. 111-125. ISSN 1311-1728 (P-ISSN) , 1314-8060 (E-ISSN) https://www.researchgate.net/publication/350432370_NUMERICAL_SOLUTION_OF_THE_TIME-FRACTIONAL_DIFFUSION_EQUATIONS_VIA_QUARTER-SWEEP_PRECONDITIONED_GAUSS-SEIDEL_METHOD http://dx.doi.org/10.12732/ijam.v34i1.5 http://dx.doi.org/10.12732/ijam.v34i1.5 |
| spellingShingle | QA1-939 Mathematics Andang Sunarto Jumat Sulaiman Chew, Jackel Vui Lung Numerical Solution of the Time-fractional Diffusion Equations via Quarter-sweep Preconditioned Gauss-seidel Method |
| title | Numerical Solution of the Time-fractional Diffusion Equations via Quarter-sweep Preconditioned Gauss-seidel Method |
| title_full | Numerical Solution of the Time-fractional Diffusion Equations via Quarter-sweep Preconditioned Gauss-seidel Method |
| title_fullStr | Numerical Solution of the Time-fractional Diffusion Equations via Quarter-sweep Preconditioned Gauss-seidel Method |
| title_full_unstemmed | Numerical Solution of the Time-fractional Diffusion Equations via Quarter-sweep Preconditioned Gauss-seidel Method |
| title_short | Numerical Solution of the Time-fractional Diffusion Equations via Quarter-sweep Preconditioned Gauss-seidel Method |
| title_sort | numerical solution of the time fractional diffusion equations via quarter sweep preconditioned gauss seidel method |
| topic | QA1-939 Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/32582/1/Numerical%20Solution%20of%20the%20Time-fractional%20Diffusion%20Equations%20via%20Quarter-sweep%20Preconditioned%20Gauss-seidel%20Method.pdf https://eprints.ums.edu.my/id/eprint/32582/3/Numerical%20Solution%20of%20the%20Time-fractional%20Diffusion%20Equations%20via%20Quarter-sweep%20Preconditioned%20Gauss-seidel%20Method%20_ABSTRACT.pdf |
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