Numerical solution on neutral delay Volterra integro-differential equation
In this research, the constant type of neutral delay Volterra integro-differential equations (NDVIDEs) are currently being resolved by applying the proposed technique in numerical analysis namely, two-point two off-step point block multistep method (2OBM4). This new technique is being applied in sol...
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| Format: | Article |
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Springer
2024
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| _version_ | 1825940198027952128 |
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| author | Ismail, Nur Inshirah Naqiah Abdul Majid, Zanariah |
| author_facet | Ismail, Nur Inshirah Naqiah Abdul Majid, Zanariah |
| author_sort | Ismail, Nur Inshirah Naqiah |
| collection | UPM |
| description | In this research, the constant type of neutral delay Volterra integro-differential equations (NDVIDEs) are currently being resolved by applying the proposed technique in numerical analysis namely, two-point two off-step point block multistep method (2OBM4). This new technique is being applied in solving NDVIDE, identified as a hybrid block multistep method, developed using Taylor series interpolating polynomials. To complete the algorithm, two alternative numerical approaches are introduced to resolve the integral and differential parts of the problems. Note that the differentiation is approximated by the divided difference formula while the integration is interpolated using composite Simpson’s rule. The proposed method has been analysed thoroughly in terms of its order, consistency, zero stability and convergence. The suitable stability region for 2OBM4 in solving NDVIDE has been constructed and the stability region is built based on the stability polynomial obtained. Consequently, numerical results are presented to demonstrate the effectiveness of the proposed 2OBM4. © The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2024. |
| first_indexed | 2024-12-09T02:24:31Z |
| format | Article |
| id | upm.eprints-112802 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-12-09T02:24:31Z |
| publishDate | 2024 |
| publisher | Springer |
| record_format | dspace |
| spelling | upm.eprints-1128022024-11-11T08:16:11Z http://psasir.upm.edu.my/id/eprint/112802/ Numerical solution on neutral delay Volterra integro-differential equation Ismail, Nur Inshirah Naqiah Abdul Majid, Zanariah In this research, the constant type of neutral delay Volterra integro-differential equations (NDVIDEs) are currently being resolved by applying the proposed technique in numerical analysis namely, two-point two off-step point block multistep method (2OBM4). This new technique is being applied in solving NDVIDE, identified as a hybrid block multistep method, developed using Taylor series interpolating polynomials. To complete the algorithm, two alternative numerical approaches are introduced to resolve the integral and differential parts of the problems. Note that the differentiation is approximated by the divided difference formula while the integration is interpolated using composite Simpson’s rule. The proposed method has been analysed thoroughly in terms of its order, consistency, zero stability and convergence. The suitable stability region for 2OBM4 in solving NDVIDE has been constructed and the stability region is built based on the stability polynomial obtained. Consequently, numerical results are presented to demonstrate the effectiveness of the proposed 2OBM4. © The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2024. Springer 2024 Article PeerReviewed Ismail, Nur Inshirah Naqiah and Abdul Majid, Zanariah (2024) Numerical solution on neutral delay Volterra integro-differential equation. Bulletin of the Malaysian Mathematical Sciences Society, 47 (3). art. no. 85. ISSN 0126-6705; eISSN: 2180-4206 https://link.springer.com/article/10.1007/s40840-024-01683-7 10.1007/s40840-024-01683-7 |
| spellingShingle | Ismail, Nur Inshirah Naqiah Abdul Majid, Zanariah Numerical solution on neutral delay Volterra integro-differential equation |
| title | Numerical solution on neutral delay Volterra integro-differential equation |
| title_full | Numerical solution on neutral delay Volterra integro-differential equation |
| title_fullStr | Numerical solution on neutral delay Volterra integro-differential equation |
| title_full_unstemmed | Numerical solution on neutral delay Volterra integro-differential equation |
| title_short | Numerical solution on neutral delay Volterra integro-differential equation |
| title_sort | numerical solution on neutral delay volterra integro differential equation |
| work_keys_str_mv | AT ismailnurinshirahnaqiah numericalsolutiononneutraldelayvolterraintegrodifferentialequation AT abdulmajidzanariah numericalsolutiononneutraldelayvolterraintegrodifferentialequation |