Efficient interpolators in implicit block method for solving delay differential equations
In this paper, the development of an implicit block method with variable stepsize variable order technique is described. The grid-point formulae for different number of blocks are derived. The block method produces two new approximations in a single integration step by using the same back values....
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| Format: | Article |
| Language: | English English |
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North Atlantic University Union
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30196/ http://psasir.upm.edu.my/id/eprint/30196/1/Efficient%20interpolators%20in%20implicit%20block%20method%20for%20solving%20delay%20differential%20equations.pdf |
| _version_ | 1848846608843669504 |
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| author | Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed |
| author_facet | Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed |
| author_sort | Ishak, Fuziyah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, the development of an implicit block
method with variable stepsize variable order technique is described. The grid-point formulae for different number of blocks are derived. The block method produces two new approximations in a single integration step by using the same back values. In order to vary the stepsize and order as efficiently as possible, the coefficients of the method at grid points are calculated and stored in the program. Delay solutions are approximated by using Lagrange and Hermite interpolations. These interpolation techniques prove to be both efficient and reliable with the two-point implicit block method in solving a wide range of delay differential equations. |
| first_indexed | 2025-11-15T09:05:25Z |
| format | Article |
| id | upm-30196 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:05:25Z |
| publishDate | 2013 |
| publisher | North Atlantic University Union |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301962015-09-21T07:44:18Z http://psasir.upm.edu.my/id/eprint/30196/ Efficient interpolators in implicit block method for solving delay differential equations Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed In this paper, the development of an implicit block method with variable stepsize variable order technique is described. The grid-point formulae for different number of blocks are derived. The block method produces two new approximations in a single integration step by using the same back values. In order to vary the stepsize and order as efficiently as possible, the coefficients of the method at grid points are calculated and stored in the program. Delay solutions are approximated by using Lagrange and Hermite interpolations. These interpolation techniques prove to be both efficient and reliable with the two-point implicit block method in solving a wide range of delay differential equations. North Atlantic University Union 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30196/1/Efficient%20interpolators%20in%20implicit%20block%20method%20for%20solving%20delay%20differential%20equations.pdf Ishak, Fuziyah and Abdul Majid, Zanariah and Suleiman, Mohamed (2013) Efficient interpolators in implicit block method for solving delay differential equations. International Journal of Mathematics and Computers in Simulation, 7 (2). pp. 116-124. ISSN 1998-0159 http://www.naun.org/cms.action?id=5359 English |
| spellingShingle | Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed Efficient interpolators in implicit block method for solving delay differential equations |
| title | Efficient interpolators in implicit block method for solving delay differential equations |
| title_full | Efficient interpolators in implicit block method for solving delay differential equations |
| title_fullStr | Efficient interpolators in implicit block method for solving delay differential equations |
| title_full_unstemmed | Efficient interpolators in implicit block method for solving delay differential equations |
| title_short | Efficient interpolators in implicit block method for solving delay differential equations |
| title_sort | efficient interpolators in implicit block method for solving delay differential equations |
| url | http://psasir.upm.edu.my/id/eprint/30196/ http://psasir.upm.edu.my/id/eprint/30196/ http://psasir.upm.edu.my/id/eprint/30196/1/Efficient%20interpolators%20in%20implicit%20block%20method%20for%20solving%20delay%20differential%20equations.pdf |