Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR
This paper will solve one of the fractional mathematical physics models, a one-dimensional time-fractional differential equation, by utilizing the second-order quarter-sweep finite-difference scheme and the preconditioned accelerated over-relaxation method. The proposed numerical method offers an...
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| Format: | Article |
| Language: | English English |
| Published: |
Springer
2021
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| Subjects: | |
| Online Access: | https://eprints.ums.edu.my/id/eprint/26832/1/Iterative%20method%20for%20solving%20abstract.pdf https://eprints.ums.edu.my/id/eprint/26832/2/Iterative%20method%20for%20solving.pdf |
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| author | Andang Sunarto Praveen Agarwal Jumat Sulaiman Vui, Jackel,Lung Chew |
| author_facet | Andang Sunarto Praveen Agarwal Jumat Sulaiman Vui, Jackel,Lung Chew |
| author_sort | Andang Sunarto |
| collection | UMS |
| description | This paper will solve one of the fractional mathematical physics models, a
one-dimensional time-fractional differential equation, by utilizing the second-order
quarter-sweep finite-difference scheme and the preconditioned accelerated
over-relaxation method. The proposed numerical method offers an efficient solution
to the time-fractional differential equation by applying the computational complexity
reduction approach by the quarter-sweep technique. The finite-difference
approximation equation will be formulated based on the Caputo’s time-fractional
derivative and quarter-sweep central difference in space. The developed
approximation equation generates a linear system on a large scale and has sparse
coefficients. With the quarter-sweep technique and the preconditioned iterative
method, computing the time-fractional differential equation solutions can be more
efficient in terms of the number of iterations and computation time. The
quarter-sweep computes a quarter of the total mesh points using the preconditioned
iterative method while maintaining the solutions’ accuracy. A numerical example will
demonstrate the efficiency of the proposed quarter-sweep preconditioned
accelerated over-relaxation method against the half-sweep preconditioned
accelerated over-relaxation, and the full-sweep preconditioned accelerated
over-relaxation methods. The numerical finding showed that the quarter-sweep finite
difference scheme and preconditioned accelerated over-relaxation method can serve
as an efficient numerical method to solve fractional differential equations. |
| first_indexed | 2024-03-06T03:06:13Z |
| format | Article |
| id | ums.eprints-26832 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:06:13Z |
| publishDate | 2021 |
| publisher | Springer |
| record_format | dspace |
| spelling | ums.eprints-268322021-04-28T07:30:32Z https://eprints.ums.edu.my/id/eprint/26832/ Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR Andang Sunarto Praveen Agarwal Jumat Sulaiman Vui, Jackel,Lung Chew QC Physics This paper will solve one of the fractional mathematical physics models, a one-dimensional time-fractional differential equation, by utilizing the second-order quarter-sweep finite-difference scheme and the preconditioned accelerated over-relaxation method. The proposed numerical method offers an efficient solution to the time-fractional differential equation by applying the computational complexity reduction approach by the quarter-sweep technique. The finite-difference approximation equation will be formulated based on the Caputo’s time-fractional derivative and quarter-sweep central difference in space. The developed approximation equation generates a linear system on a large scale and has sparse coefficients. With the quarter-sweep technique and the preconditioned iterative method, computing the time-fractional differential equation solutions can be more efficient in terms of the number of iterations and computation time. The quarter-sweep computes a quarter of the total mesh points using the preconditioned iterative method while maintaining the solutions’ accuracy. A numerical example will demonstrate the efficiency of the proposed quarter-sweep preconditioned accelerated over-relaxation method against the half-sweep preconditioned accelerated over-relaxation, and the full-sweep preconditioned accelerated over-relaxation methods. The numerical finding showed that the quarter-sweep finite difference scheme and preconditioned accelerated over-relaxation method can serve as an efficient numerical method to solve fractional differential equations. Springer 2021 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/26832/1/Iterative%20method%20for%20solving%20abstract.pdf text en https://eprints.ums.edu.my/id/eprint/26832/2/Iterative%20method%20for%20solving.pdf Andang Sunarto and Praveen Agarwal and Jumat Sulaiman and Vui, Jackel,Lung Chew (2021) Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR. (Submitted) https://doi.org/10.1186/s13662-021-03310-2 |
| spellingShingle | QC Physics Andang Sunarto Praveen Agarwal Jumat Sulaiman Vui, Jackel,Lung Chew Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR |
| title | Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR |
| title_full | Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR |
| title_fullStr | Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR |
| title_full_unstemmed | Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR |
| title_short | Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR |
| title_sort | iterative method for solving one dimensional fractional mathematical physics model via quarter sweep and paor |
| topic | QC Physics |
| url | https://eprints.ums.edu.my/id/eprint/26832/1/Iterative%20method%20for%20solving%20abstract.pdf https://eprints.ums.edu.my/id/eprint/26832/2/Iterative%20method%20for%20solving.pdf |
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