Numerical approach for delay Volterra integro-differential equation
The delay integro-differential equation for the Volterra type has been solved by using the two-point multistep block (2PBM) method with constant step-size. The proposed block method of order three is formulated using Taylor expansion and will simultaneously approximate the numerical solution at two...
| Main Authors: | , , , |
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| Format: | Article |
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Universiti Kebangsaan Malaysia
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/102337/ |
| _version_ | 1848863776664715264 |
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| author | Baharum, Nur Auni Abdul Majid, Zanariah Senu, Norazak Rosali, Haliza |
| author_facet | Baharum, Nur Auni Abdul Majid, Zanariah Senu, Norazak Rosali, Haliza |
| author_sort | Baharum, Nur Auni |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The delay integro-differential equation for the Volterra type has been solved by using the two-point multistep block (2PBM) method with constant step-size. The proposed block method of order three is formulated using Taylor expansion and will simultaneously approximate the numerical solution at two points. The 2PBM method is developed by combining the predictor and corrector formulae in the PECE mode. The predictor formulae are explicit, while the corrector formulae are implicit. The algorithm for the approximate solutions were constructed and analyzed using the 2PBM method with Newton-Cotes quadrature rules. This paper focused on constant and pantograph delay types, and the previous values are used to interpolate the delay solutions. Moreover, the studies also carried out on the stability analysis of the proposed method. Some numerical results are tested to validate the competency of the multistep block method with quadrature rule approach. |
| first_indexed | 2025-11-15T13:38:18Z |
| format | Article |
| id | upm-102337 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:38:18Z |
| publishDate | 2022 |
| publisher | Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1023372024-04-04T03:31:19Z http://psasir.upm.edu.my/id/eprint/102337/ Numerical approach for delay Volterra integro-differential equation Baharum, Nur Auni Abdul Majid, Zanariah Senu, Norazak Rosali, Haliza The delay integro-differential equation for the Volterra type has been solved by using the two-point multistep block (2PBM) method with constant step-size. The proposed block method of order three is formulated using Taylor expansion and will simultaneously approximate the numerical solution at two points. The 2PBM method is developed by combining the predictor and corrector formulae in the PECE mode. The predictor formulae are explicit, while the corrector formulae are implicit. The algorithm for the approximate solutions were constructed and analyzed using the 2PBM method with Newton-Cotes quadrature rules. This paper focused on constant and pantograph delay types, and the previous values are used to interpolate the delay solutions. Moreover, the studies also carried out on the stability analysis of the proposed method. Some numerical results are tested to validate the competency of the multistep block method with quadrature rule approach. Universiti Kebangsaan Malaysia 2022 Article PeerReviewed Baharum, Nur Auni and Abdul Majid, Zanariah and Senu, Norazak and Rosali, Haliza (2022) Numerical approach for delay Volterra integro-differential equation. Sains Malaysiana, 51 (12). pp. 4125-4144. ISSN 0126-6039; ESSN: 2735-0118 https://www.ukm.my/jsm/english_journals/vol51num12_2022/contentsVol51num12_2022.html 10.17576/jsm-2022-5112-20 |
| spellingShingle | Baharum, Nur Auni Abdul Majid, Zanariah Senu, Norazak Rosali, Haliza Numerical approach for delay Volterra integro-differential equation |
| title | Numerical approach for delay Volterra integro-differential equation |
| title_full | Numerical approach for delay Volterra integro-differential equation |
| title_fullStr | Numerical approach for delay Volterra integro-differential equation |
| title_full_unstemmed | Numerical approach for delay Volterra integro-differential equation |
| title_short | Numerical approach for delay Volterra integro-differential equation |
| title_sort | numerical approach for delay volterra integro-differential equation |
| url | http://psasir.upm.edu.my/id/eprint/102337/ http://psasir.upm.edu.my/id/eprint/102337/ http://psasir.upm.edu.my/id/eprint/102337/ |