Hybrid multistep block method for solving neutral Volterra integro-differential equation with proportional and mixed delays
The neutral Volterra integro-differential equation with proportional and mixed delays (NDVIDE) is being solved by a newly proposed technique in numerical method, namely, the two-point one off-point block multistep method (1OBM3). The method is also known as a hybrid multistep block method. Subsequen...
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| Format: | Article |
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Penerbit Universiti Kebangsaan Malaysia (UKM Press)
2023
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| Online Access: | http://psasir.upm.edu.my/id/eprint/108222/ |
| _version_ | 1848865105345773568 |
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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 |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The neutral Volterra integro-differential equation with proportional and mixed delays (NDVIDE) is being solved by a newly proposed technique in numerical method, namely, the two-point one off-point block multistep method (1OBM3). The method is also known as a hybrid multistep block method. Subsequently, Lagrange interpolating polynomial is utilized in order to develop the hybrid block method. The foundation of the technique is taken from predictor and corrector formulae. The proposed method will solve NDVIDE in two steps simultaneously, with three predictor formulae including one off-point. The NDVIDE problems are solved via the constant step size technique. In order to solve the integral and differential parts of the problems, two alternative numerical approaches are applied. The differentiation part is approximated by deriving the divided difference formula, while the integration part is interpolated using composite Simpson’s rule. Note that the proposed method has been analysed thoroughly regarding its order, consistency, zero stability and convergence of the method. The stability region for 1OBM3 has been constructed based on the stability polynomial obtained. Consequently, numerical results are presented to demonstrate the effectiveness of the proposed method, 1OBM3. |
| first_indexed | 2025-11-15T13:59:25Z |
| format | Article |
| id | upm-108222 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:59:25Z |
| publishDate | 2023 |
| publisher | Penerbit Universiti Kebangsaan Malaysia (UKM Press) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1082222024-09-11T06:44:47Z http://psasir.upm.edu.my/id/eprint/108222/ Hybrid multistep block method for solving neutral Volterra integro-differential equation with proportional and mixed delays Ismail, Nur Inshirah Naqiah Abdul Majid, Zanariah The neutral Volterra integro-differential equation with proportional and mixed delays (NDVIDE) is being solved by a newly proposed technique in numerical method, namely, the two-point one off-point block multistep method (1OBM3). The method is also known as a hybrid multistep block method. Subsequently, Lagrange interpolating polynomial is utilized in order to develop the hybrid block method. The foundation of the technique is taken from predictor and corrector formulae. The proposed method will solve NDVIDE in two steps simultaneously, with three predictor formulae including one off-point. The NDVIDE problems are solved via the constant step size technique. In order to solve the integral and differential parts of the problems, two alternative numerical approaches are applied. The differentiation part is approximated by deriving the divided difference formula, while the integration part is interpolated using composite Simpson’s rule. Note that the proposed method has been analysed thoroughly regarding its order, consistency, zero stability and convergence of the method. The stability region for 1OBM3 has been constructed based on the stability polynomial obtained. Consequently, numerical results are presented to demonstrate the effectiveness of the proposed method, 1OBM3. Penerbit Universiti Kebangsaan Malaysia (UKM Press) 2023 Article PeerReviewed Ismail, Nur Inshirah Naqiah and Abdul Majid, Zanariah (2023) Hybrid multistep block method for solving neutral Volterra integro-differential equation with proportional and mixed delays. Sains Malaysiana, 52 (8). pp. 2337-2351. ISSN 0126-6039; ESSN:2735-0118 https://www.ukm.my/jsm/english_journals/vol52num8_2023/contentsVol52num8_2023.html 10.17576/jsm-2023-5208-13 |
| spellingShingle | Ismail, Nur Inshirah Naqiah Abdul Majid, Zanariah Hybrid multistep block method for solving neutral Volterra integro-differential equation with proportional and mixed delays |
| title | Hybrid multistep block method for solving neutral Volterra integro-differential equation with proportional and mixed delays |
| title_full | Hybrid multistep block method for solving neutral Volterra integro-differential equation with proportional and mixed delays |
| title_fullStr | Hybrid multistep block method for solving neutral Volterra integro-differential equation with proportional and mixed delays |
| title_full_unstemmed | Hybrid multistep block method for solving neutral Volterra integro-differential equation with proportional and mixed delays |
| title_short | Hybrid multistep block method for solving neutral Volterra integro-differential equation with proportional and mixed delays |
| title_sort | hybrid multistep block method for solving neutral volterra integro-differential equation with proportional and mixed delays |
| url | http://psasir.upm.edu.my/id/eprint/108222/ http://psasir.upm.edu.my/id/eprint/108222/ http://psasir.upm.edu.my/id/eprint/108222/ |