Diagonally multistep block method for solving Volterra integro-differential equation with delay
Volterra integro-differential equation with delay (VIDED) is solved using a diagonally multistep block method (DMB). This study provides the derivation of the DMB utilizing Taylor series with a constant step size strategy for treating the first order VIDED. In predictor-corrector mode,...
| Main Authors: | , , , |
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| Format: | Article |
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Malaysian Mathematical Society
2023
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| Online Access: | http://psasir.upm.edu.my/id/eprint/107328/ |
| _version_ | 1848864873100869632 |
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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 | Volterra integro-differential equation with delay (VIDED) is solved using a diagonally multistep block method (DMB). This study provides the derivation of the DMB utilizing Taylor series with a constant step size strategy for treating the first order VIDED. In predictor-corrector mode, the DMB method combines the predictor and corrector formulae. It approximates two numerical solutions simultaneously within a block. The algorithm for the approximation solution is developed and the Newton-Cotes formulae are adapted in the DMB method to estimate the solution for an integral component. Theoretically, the consistency and zero stability that led to convergence properties are examined. The stability region also has been plotted. The numerical results indicate that the developed method is superior in terms of the number of steps, accuracy and computation time taken. |
| first_indexed | 2025-11-15T13:55:43Z |
| format | Article |
| id | upm-107328 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:55:43Z |
| publishDate | 2023 |
| publisher | Malaysian Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1073282024-10-15T06:45:34Z http://psasir.upm.edu.my/id/eprint/107328/ Diagonally multistep block method for solving Volterra integro-differential equation with delay Baharum, Nur Auni Abdul Majid, Zanariah Senu, Norazak Rosali, Haliza Volterra integro-differential equation with delay (VIDED) is solved using a diagonally multistep block method (DMB). This study provides the derivation of the DMB utilizing Taylor series with a constant step size strategy for treating the first order VIDED. In predictor-corrector mode, the DMB method combines the predictor and corrector formulae. It approximates two numerical solutions simultaneously within a block. The algorithm for the approximation solution is developed and the Newton-Cotes formulae are adapted in the DMB method to estimate the solution for an integral component. Theoretically, the consistency and zero stability that led to convergence properties are examined. The stability region also has been plotted. The numerical results indicate that the developed method is superior in terms of the number of steps, accuracy and computation time taken. Malaysian Mathematical Society 2023 Article PeerReviewed Baharum, Nur Auni and Abdul Majid, Zanariah and Senu, Norazak and Rosali, Haliza (2023) Diagonally multistep block method for solving Volterra integro-differential equation with delay. Menemui Matematik, 45 (2). pp. 208-223. ISSN 0126-9003 https://myjms.mohe.gov.my/index.php/dismath/article/view/23137 |
| spellingShingle | Baharum, Nur Auni Abdul Majid, Zanariah Senu, Norazak Rosali, Haliza Diagonally multistep block method for solving Volterra integro-differential equation with delay |
| title | Diagonally multistep block method for solving Volterra integro-differential equation with delay |
| title_full | Diagonally multistep block method for solving Volterra integro-differential equation with delay |
| title_fullStr | Diagonally multistep block method for solving Volterra integro-differential equation with delay |
| title_full_unstemmed | Diagonally multistep block method for solving Volterra integro-differential equation with delay |
| title_short | Diagonally multistep block method for solving Volterra integro-differential equation with delay |
| title_sort | diagonally multistep block method for solving volterra integro-differential equation with delay |
| url | http://psasir.upm.edu.my/id/eprint/107328/ http://psasir.upm.edu.my/id/eprint/107328/ |