Solving delay differential equations of small and vanishing lag using multistep block method
This paper considers the numerical solution of delay differential equations for solving the problem of small and vanishing lag using multistep block method. This problem arises when the size of a delay value is smaller than the step size, x - τ < h, and the delay time may even vanish when τ → 0 i...
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/51855/ http://psasir.upm.edu.my/id/eprint/51855/1/51855.pdf |
| _version_ | 1848851946621894656 |
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| author | Abdul Aziz, Nurul Huda Abdul Majid, Zanariah Ismail, Fudziah |
| author_facet | Abdul Aziz, Nurul Huda Abdul Majid, Zanariah Ismail, Fudziah |
| author_sort | Abdul Aziz, Nurul Huda |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper considers the numerical solution of delay differential equations for solving the problem of small and vanishing lag using multistep block method. This problem arises when the size of a delay value is smaller than the step size, x - τ < h, and the delay time may even vanish when τ → 0 in a current step. The proposed approach that is based on interpolation of Newton divided difference has been implemented by adapting this problem to the multistep block method. In order to achieve the required accuracy, this approach considered the appropriate degree of interpolation polynomial in approximating the solution of delay term. The developed code for solving small and vanishing lag is done using C program and we called it as DDEB5. The P-stability and Q-stability of this method are also studied. Numerical results are presented and compared to the existing method in order to illustrate the efficiency of the proposed method. |
| first_indexed | 2025-11-15T10:30:16Z |
| format | Article |
| id | upm-51855 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:30:16Z |
| publishDate | 2014 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-518552017-05-02T08:05:13Z http://psasir.upm.edu.my/id/eprint/51855/ Solving delay differential equations of small and vanishing lag using multistep block method Abdul Aziz, Nurul Huda Abdul Majid, Zanariah Ismail, Fudziah This paper considers the numerical solution of delay differential equations for solving the problem of small and vanishing lag using multistep block method. This problem arises when the size of a delay value is smaller than the step size, x - τ < h, and the delay time may even vanish when τ → 0 in a current step. The proposed approach that is based on interpolation of Newton divided difference has been implemented by adapting this problem to the multistep block method. In order to achieve the required accuracy, this approach considered the appropriate degree of interpolation polynomial in approximating the solution of delay term. The developed code for solving small and vanishing lag is done using C program and we called it as DDEB5. The P-stability and Q-stability of this method are also studied. Numerical results are presented and compared to the existing method in order to illustrate the efficiency of the proposed method. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51855/1/51855.pdf Abdul Aziz, Nurul Huda and Abdul Majid, Zanariah and Ismail, Fudziah (2014) Solving delay differential equations of small and vanishing lag using multistep block method. Journal of Applied Mathematics, 2014. art. no. 348912. pp. 1-10. ISSN 1110-757X; ESSN: 1687-0042 https://www.hindawi.com/journals/jam/2014/348912/abs/ 10.1155/2014/348912 |
| spellingShingle | Abdul Aziz, Nurul Huda Abdul Majid, Zanariah Ismail, Fudziah Solving delay differential equations of small and vanishing lag using multistep block method |
| title | Solving delay differential equations of small and vanishing lag using multistep block method |
| title_full | Solving delay differential equations of small and vanishing lag using multistep block method |
| title_fullStr | Solving delay differential equations of small and vanishing lag using multistep block method |
| title_full_unstemmed | Solving delay differential equations of small and vanishing lag using multistep block method |
| title_short | Solving delay differential equations of small and vanishing lag using multistep block method |
| title_sort | solving delay differential equations of small and vanishing lag using multistep block method |
| url | http://psasir.upm.edu.my/id/eprint/51855/ http://psasir.upm.edu.my/id/eprint/51855/ http://psasir.upm.edu.my/id/eprint/51855/ http://psasir.upm.edu.my/id/eprint/51855/1/51855.pdf |