Variable step size and order strategy for delay differential equations in PIE(CIE)s mode
This article deals with the strategy of variable step size and variable order implementation that has been formulated for solving first order of delay differential equations. This strategy is adapted in PIE(CIE)s mode which is generally based on predictor-corrector scheme in multistep block method o...
| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57588/1/Variable%20step%20size%20and%20order%20strategy%20for%20delay%20differential%20equations%20in%20PIE%28CIE%29s%20mode.pdf |
| _version_ | 1796976724171292672 |
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| author | Abdul Aziz, Nurul Huda Abdul Majid, Zanariah |
| author_facet | Abdul Aziz, Nurul Huda Abdul Majid, Zanariah |
| author_sort | Abdul Aziz, Nurul Huda |
| collection | UPM |
| description | This article deals with the strategy of variable step size and variable order implementation that has been formulated for solving first order of delay differential equations. This strategy is adapted in PIE(CIE)s mode which is generally based on predictor-corrector scheme in multistep block method of order 4 to 9 with s is for convergence test. The purpose here is to enhance the efficiency of the developed predictor-corrector algorithm in the capability to vary automatically not only for the step size, but the order of the method employed as well. All order and coefficients are stored in the code in order to avoid an expensive computational work. The delay argument would be evaluated using Newton divided-difference interpolation at which the points involved would be similar to the current order of the method. Illustrative examples are included to demonstrate the validity and applicability of the presented strategy and comparison is made with the existing results. |
| first_indexed | 2024-03-06T09:29:51Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57588 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:29:51Z |
| publishDate | 2014 |
| publisher | AIP Publishing LLC |
| record_format | dspace |
| spelling | upm.eprints-575882017-10-24T06:07:19Z http://psasir.upm.edu.my/id/eprint/57588/ Variable step size and order strategy for delay differential equations in PIE(CIE)s mode Abdul Aziz, Nurul Huda Abdul Majid, Zanariah This article deals with the strategy of variable step size and variable order implementation that has been formulated for solving first order of delay differential equations. This strategy is adapted in PIE(CIE)s mode which is generally based on predictor-corrector scheme in multistep block method of order 4 to 9 with s is for convergence test. The purpose here is to enhance the efficiency of the developed predictor-corrector algorithm in the capability to vary automatically not only for the step size, but the order of the method employed as well. All order and coefficients are stored in the code in order to avoid an expensive computational work. The delay argument would be evaluated using Newton divided-difference interpolation at which the points involved would be similar to the current order of the method. Illustrative examples are included to demonstrate the validity and applicability of the presented strategy and comparison is made with the existing results. AIP Publishing LLC 2014 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57588/1/Variable%20step%20size%20and%20order%20strategy%20for%20delay%20differential%20equations%20in%20PIE%28CIE%29s%20mode.pdf Abdul Aziz, Nurul Huda and Abdul Majid, Zanariah (2014) Variable step size and order strategy for delay differential equations in PIE(CIE)s mode. In: 3rd International Conference on Quantitative Sciences and Its Applications (ICOQSIA 2014), 12–14 Aug. 2014, Langkawi, Kedah. (pp. 58-64). 10.1063/1.4903563 |
| spellingShingle | Abdul Aziz, Nurul Huda Abdul Majid, Zanariah Variable step size and order strategy for delay differential equations in PIE(CIE)s mode |
| title | Variable step size and order strategy for delay differential equations in PIE(CIE)s mode |
| title_full | Variable step size and order strategy for delay differential equations in PIE(CIE)s mode |
| title_fullStr | Variable step size and order strategy for delay differential equations in PIE(CIE)s mode |
| title_full_unstemmed | Variable step size and order strategy for delay differential equations in PIE(CIE)s mode |
| title_short | Variable step size and order strategy for delay differential equations in PIE(CIE)s mode |
| title_sort | variable step size and order strategy for delay differential equations in pie cie s mode |
| url | http://psasir.upm.edu.my/id/eprint/57588/1/Variable%20step%20size%20and%20order%20strategy%20for%20delay%20differential%20equations%20in%20PIE%28CIE%29s%20mode.pdf |
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