Solving delay differential equations by the five-point one-step block method using Neville's interpolation
A five-point one-step block method based on the Newton backward divided difference formulae for the solution of first-order delay differential equations is derived. The proposed block method will approximate the solutions of initial value problems at five points simultaneously using variable step si...
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| Format: | Article |
| Language: | English English |
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Taylor & Francis
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30190/ http://psasir.upm.edu.my/id/eprint/30190/1/Solving%20delay%20differential%20equations%20by%20the%20five.pdf |
| _version_ | 1848846607175385088 |
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| author | Abdul Majid, Zanariah Mohd Radzi, Hazwani Ismail, Fudziah |
| author_facet | Abdul Majid, Zanariah Mohd Radzi, Hazwani Ismail, Fudziah |
| author_sort | Abdul Majid, Zanariah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A five-point one-step block method based on the Newton backward divided difference formulae for the solution of first-order delay differential equations is derived. The proposed block method will approximate the solutions of initial value problems at five points simultaneously using variable step size. The approximation of the delay term is calculated using Neville's interpolation. The block method will be formulated in terms of linear multistep method, but the method is equivalent to one-step method. The order of the block method will be discussed. The P-stability and Q-stability regions of the block method using Neville's interpolation for the delay term are presented for a fixed step size. Numerical results are given to show the efficiency of the proposed method and compared with the existing method. |
| first_indexed | 2025-11-15T09:05:24Z |
| format | Article |
| id | upm-30190 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:05:24Z |
| publishDate | 2013 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301902015-09-18T07:24:28Z http://psasir.upm.edu.my/id/eprint/30190/ Solving delay differential equations by the five-point one-step block method using Neville's interpolation Abdul Majid, Zanariah Mohd Radzi, Hazwani Ismail, Fudziah A five-point one-step block method based on the Newton backward divided difference formulae for the solution of first-order delay differential equations is derived. The proposed block method will approximate the solutions of initial value problems at five points simultaneously using variable step size. The approximation of the delay term is calculated using Neville's interpolation. The block method will be formulated in terms of linear multistep method, but the method is equivalent to one-step method. The order of the block method will be discussed. The P-stability and Q-stability regions of the block method using Neville's interpolation for the delay term are presented for a fixed step size. Numerical results are given to show the efficiency of the proposed method and compared with the existing method. Taylor & Francis 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30190/1/Solving%20delay%20differential%20equations%20by%20the%20five.pdf Abdul Majid, Zanariah and Mohd Radzi, Hazwani and Ismail, Fudziah (2013) Solving delay differential equations by the five-point one-step block method using Neville's interpolation. International Journal of Computer Mathematics , 90 (7). pp. 1459-1470. ISSN 0020-7160 10.1080/00207160.2012.754015 English |
| spellingShingle | Abdul Majid, Zanariah Mohd Radzi, Hazwani Ismail, Fudziah Solving delay differential equations by the five-point one-step block method using Neville's interpolation |
| title | Solving delay differential equations by the five-point one-step block method using Neville's interpolation |
| title_full | Solving delay differential equations by the five-point one-step block method using Neville's interpolation |
| title_fullStr | Solving delay differential equations by the five-point one-step block method using Neville's interpolation |
| title_full_unstemmed | Solving delay differential equations by the five-point one-step block method using Neville's interpolation |
| title_short | Solving delay differential equations by the five-point one-step block method using Neville's interpolation |
| title_sort | solving delay differential equations by the five-point one-step block method using neville's interpolation |
| url | http://psasir.upm.edu.my/id/eprint/30190/ http://psasir.upm.edu.my/id/eprint/30190/ http://psasir.upm.edu.my/id/eprint/30190/1/Solving%20delay%20differential%20equations%20by%20the%20five.pdf |