QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems
Two-point boundary value problems are commonly used as a numerical test in developing an efficient numerical method. Several researchers studied the application of a cubic non-polynomial spline method to solve the two-point boundary value problems. A preliminary study found that a cubic non-polynomi...
| Main Authors: | , , , , |
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| Format: | Proceedings |
| Language: | English English |
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IOP Publishing Ltd.
2021
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| Online Access: | https://eprints.ums.edu.my/id/eprint/32519/1/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/32519/2/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.pdf |
| _version_ | 1825714707697238016 |
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| author | A Sunarto P Agarwal Jackel Vui Lung Chew H Justine Jumat Sulaiman |
| author_facet | A Sunarto P Agarwal Jackel Vui Lung Chew H Justine Jumat Sulaiman |
| author_sort | A Sunarto |
| collection | UMS |
| description | Two-point boundary value problems are commonly used as a numerical test in developing an efficient numerical method. Several researchers studied the application of a cubic non-polynomial spline method to solve the two-point boundary value problems. A preliminary study found that a cubic non-polynomial spline method is better than a standard finite difference method in terms of the accuracy of the solution. Therefore, this paper aims to examine the performance of a cubic non-polynomial spline method through the combination with the full-, half-, and quarter-sweep iterations. The performance was evaluated in terms of the number of iterations, the execution time and the maximum absolute error by varying the iterations from full-, half- to quarter-sweep. A successive over-relaxation iterative method was implemented to solve the large and sparse linear system. The numerical result showed that the newly derived QSSOR method, based on a cubic non-polynomial spline, performed better than the tested FSSOR and HSSOR methods. |
| first_indexed | 2024-03-06T03:15:49Z |
| format | Proceedings |
| id | ums.eprints-32519 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:15:49Z |
| publishDate | 2021 |
| publisher | IOP Publishing Ltd. |
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| spelling | ums.eprints-325192022-05-03T13:14:55Z https://eprints.ums.edu.my/id/eprint/32519/ QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems A Sunarto P Agarwal Jackel Vui Lung Chew H Justine Jumat Sulaiman QA101-(145) Elementary mathematics. Arithmetic Two-point boundary value problems are commonly used as a numerical test in developing an efficient numerical method. Several researchers studied the application of a cubic non-polynomial spline method to solve the two-point boundary value problems. A preliminary study found that a cubic non-polynomial spline method is better than a standard finite difference method in terms of the accuracy of the solution. Therefore, this paper aims to examine the performance of a cubic non-polynomial spline method through the combination with the full-, half-, and quarter-sweep iterations. The performance was evaluated in terms of the number of iterations, the execution time and the maximum absolute error by varying the iterations from full-, half- to quarter-sweep. A successive over-relaxation iterative method was implemented to solve the large and sparse linear system. The numerical result showed that the newly derived QSSOR method, based on a cubic non-polynomial spline, performed better than the tested FSSOR and HSSOR methods. IOP Publishing Ltd. 2021 Proceedings PeerReviewed text en https://eprints.ums.edu.my/id/eprint/32519/1/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/32519/2/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.pdf A Sunarto and P Agarwal and Jackel Vui Lung Chew and H Justine and Jumat Sulaiman (2021) QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems. https://iopscience.iop.org/article/10.1088/1742-6596/2000/1/012007 |
| spellingShingle | QA101-(145) Elementary mathematics. Arithmetic A Sunarto P Agarwal Jackel Vui Lung Chew H Justine Jumat Sulaiman QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems |
| title | QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems |
| title_full | QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems |
| title_fullStr | QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems |
| title_full_unstemmed | QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems |
| title_short | QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems |
| title_sort | qssor and cubic non polynomial spline method for the solution of two point boundary value problems |
| topic | QA101-(145) Elementary mathematics. Arithmetic |
| url | https://eprints.ums.edu.my/id/eprint/32519/1/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/32519/2/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.pdf |
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