Numerical solution and stability of multistep method for solving delay differential equations.
This paper considers the numerical solution of delay differential equations. The predictor–corrector scheme based on generalized multistep methods are implemented in variable order variable stepsize techniques. The formulae are represented in divided difference form where the integration coefficient...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
JJIAM Publishing Committee and Springer
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/15861/ |
| _version_ | 1848842797834043392 |
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| author | Suleiman, Mohamed B. Ishak, Fuziyah |
| author_facet | Suleiman, Mohamed B. Ishak, Fuziyah |
| author_sort | Suleiman, Mohamed B. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper considers the numerical solution of delay differential equations. The predictor–corrector scheme based on generalized multistep methods are implemented in variable order variable stepsize techniques. The formulae are represented in divided difference form where the integration coefficients are computed by a simple recurrence relation. This representation produces simpler calculation as compared with the modified divided difference form, but no sacrifice is made in efficiency
and accuracy of the method. Numerical results prove that the method is reliable, efficient and accurate. The P- and Q-stability regions for a fixed stepsize of the predictor–corrector scheme are illustrated for various orders. |
| first_indexed | 2025-11-15T08:04:51Z |
| format | Article |
| id | upm-15861 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:04:51Z |
| publishDate | 2010 |
| publisher | JJIAM Publishing Committee and Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-158612013-07-25T07:22:14Z http://psasir.upm.edu.my/id/eprint/15861/ Numerical solution and stability of multistep method for solving delay differential equations. Suleiman, Mohamed B. Ishak, Fuziyah This paper considers the numerical solution of delay differential equations. The predictor–corrector scheme based on generalized multistep methods are implemented in variable order variable stepsize techniques. The formulae are represented in divided difference form where the integration coefficients are computed by a simple recurrence relation. This representation produces simpler calculation as compared with the modified divided difference form, but no sacrifice is made in efficiency and accuracy of the method. Numerical results prove that the method is reliable, efficient and accurate. The P- and Q-stability regions for a fixed stepsize of the predictor–corrector scheme are illustrated for various orders. JJIAM Publishing Committee and Springer 2010-12 Article PeerReviewed Suleiman, Mohamed B. and Ishak, Fuziyah (2010) Numerical solution and stability of multistep method for solving delay differential equations. Japan Journal of Industrial and Applied Mathematics, 27 (3). pp. 395-410. ISSN 1868-937X 10.1007/s13160-010-0017-6 English |
| spellingShingle | Suleiman, Mohamed B. Ishak, Fuziyah Numerical solution and stability of multistep method for solving delay differential equations. |
| title | Numerical solution and stability of multistep method for solving delay differential equations. |
| title_full | Numerical solution and stability of multistep method for solving delay differential equations. |
| title_fullStr | Numerical solution and stability of multistep method for solving delay differential equations. |
| title_full_unstemmed | Numerical solution and stability of multistep method for solving delay differential equations. |
| title_short | Numerical solution and stability of multistep method for solving delay differential equations. |
| title_sort | numerical solution and stability of multistep method for solving delay differential equations. |
| url | http://psasir.upm.edu.my/id/eprint/15861/ http://psasir.upm.edu.my/id/eprint/15861/ |