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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,...

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Main Authors: Baharum, Nur Auni, Abdul Majid, Zanariah, Senu, Norazak, Rosali, Haliza
Format: Article
Published: Malaysian Mathematical Society 2023
Online Access:http://psasir.upm.edu.my/id/eprint/107328/
https://myjms.mohe.gov.my/index.php/dismath/article/view/23137
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spelling my.upm.eprints.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
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.
format Article
author Baharum, Nur Auni
Abdul Majid, Zanariah
Senu, Norazak
Rosali, Haliza
spellingShingle Baharum, Nur Auni
Abdul Majid, Zanariah
Senu, Norazak
Rosali, Haliza
Diagonally multistep block method for solving Volterra integro-differential equation with delay
author_facet Baharum, Nur Auni
Abdul Majid, Zanariah
Senu, Norazak
Rosali, Haliza
author_sort Baharum, Nur Auni
title 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_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_sort diagonally multistep block method for solving volterra integro-differential equation with delay
publisher Malaysian Mathematical Society
publishDate 2023
url http://psasir.upm.edu.my/id/eprint/107328/
https://myjms.mohe.gov.my/index.php/dismath/article/view/23137
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score 13.251813

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