The implicit multistep block method with an off-step point for initial value problems of neutral delay Volterra integro-differential equations
The aim of this manuscript is to solve the initial-value problems of neutral delay Volterra integro-differential equations with constant or proportional delays. Hence, a proposed hybrid technique named as an implicit multistep block method with an off-step point (1OBM4) is formulated for the numeric...
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Institute for Mathematical Research, Universiti Putra Malaysia
2023
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my.upm.eprints.1101562024-09-05T06:50:34Z http://psasir.upm.edu.my/id/eprint/110156/ The implicit multistep block method with an off-step point for initial value problems of neutral delay Volterra integro-differential equations Ismail, N. I. N. Majid, Z. A. The aim of this manuscript is to solve the initial-value problems of neutral delay Volterra integro-differential equations with constant or proportional delays. Hence, a proposed hybrid technique named as an implicit multistep block method with an off-step point (1OBM4) is formulated for the numerical solution of NDVIDE. A LMM associated with an off-point is known as hybrid LMM. The proposed technique, 1OBM4, attempts to solve the problem synchronously in a block manner. Moreover, a Taylor expansion is implemented to develop 1OBM4 in predictor-corrector mode. Two different approaches are presented in order to solve both integral and differential parts of the problem. Some analyses on 1OBM4 are considered in terms of order and convergence of the method. A stability polynomial is also obtained for the stability regions to be constructed. In the last section, some numerical results are demonstrated to show the applicability of 1OBM4 in solving NDVIDE with constant or proportional delays. Institute for Mathematical Research, Universiti Putra Malaysia 2023 Article PeerReviewed Ismail, N. I. N. and Majid, Z. A. (2023) The implicit multistep block method with an off-step point for initial value problems of neutral delay Volterra integro-differential equations. Malaysian Journal Of Mathematical Sciences, 17 (3). art. no. 15. pp. 487-508. ISSN 1823-8343; ESSN: 2289-750X https://mjms.upm.edu.my/lihatmakalah.php?kod=2023/September/17/3/487-508 10.47836/mjms.17.3.15 |
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The aim of this manuscript is to solve the initial-value problems of neutral delay Volterra integro-differential equations with constant or proportional delays. Hence, a proposed hybrid technique named as an implicit multistep block method with an off-step point (1OBM4) is formulated for the numerical solution of NDVIDE. A LMM associated with an off-point is known as hybrid LMM. The proposed technique, 1OBM4, attempts to solve the problem synchronously in a block manner. Moreover, a Taylor expansion is implemented to develop 1OBM4 in predictor-corrector mode. Two different approaches are presented in order to solve both integral and differential parts of the problem. Some analyses on 1OBM4 are considered in terms of order and convergence of the method. A stability polynomial is also obtained for the stability regions to be constructed. In the last section, some numerical results are demonstrated to show the applicability of 1OBM4 in solving NDVIDE with constant or proportional delays. |
| format |
Article |
| author |
Ismail, N. I. N. Majid, Z. A. |
| spellingShingle |
Ismail, N. I. N. Majid, Z. A. The implicit multistep block method with an off-step point for initial value problems of neutral delay Volterra integro-differential equations |
| author_facet |
Ismail, N. I. N. Majid, Z. A. |
| author_sort |
Ismail, N. I. N. |
| title |
The implicit multistep block method with an off-step point for initial value problems of neutral delay Volterra integro-differential equations |
| title_short |
The implicit multistep block method with an off-step point for initial value problems of neutral delay Volterra integro-differential equations |
| title_full |
The implicit multistep block method with an off-step point for initial value problems of neutral delay Volterra integro-differential equations |
| title_fullStr |
The implicit multistep block method with an off-step point for initial value problems of neutral delay Volterra integro-differential equations |
| title_full_unstemmed |
The implicit multistep block method with an off-step point for initial value problems of neutral delay Volterra integro-differential equations |
| title_sort |
implicit multistep block method with an off-step point for initial value problems of neutral delay volterra integro-differential equations |
| publisher |
Institute for Mathematical Research, Universiti Putra Malaysia |
| publishDate |
2023 |
| url |
http://psasir.upm.edu.my/id/eprint/110156/ https://mjms.upm.edu.my/lihatmakalah.php?kod=2023/September/17/3/487-508 |
| _version_ |
1811686052910333952 |
| score |
13.251813 |