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Volume 14, Issue 5
Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method

Nur Inshirah Naqiah Ismail, Zanariah Abdul Majid & Norazak Senu

Adv. Appl. Math. Mech., 14 (2022), pp. 1138-1160.

Published online: 2022-06

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  • Abstract

Neutral Delay Differential Equation (NDDE) is a differential problem that has regularly existed in numerous occurrences and has represented a significant role in dealing with real-life phenomena, especially on their application in biological and physiological processes. A fifth-order two-point hybrid implicit multistep block method (2PIH5) has been formulated in this research for the numerical solution of Neutral Delay Differential Equation (NDDE). A Taylor series interpolation polynomial has been implemented in the formulation of the proposed 2PIH5. The order, consistency, and zero-stability for 2PIH5 have been illustrated. The analyses of convergence and stability test have been performed and discussed. The initial value problems for the first-order NDDE with constant or proportional delay have been solved using the proposed block method. Some numerical results for the proposed method have been presented to prove the adaptability and applicability of the proposed method in solving NDDE. The proposed method is proved to be comparable with the other existing methods. It is assumed to be reliable and efficient for solving the first-order NDDE with constant or proportional delay.

  • Keywords

Constant delay, hybrid method, multistep block method, neutral delay differential equation, proportional delay.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-1138, author = {Nur Inshirah Naqiah and Ismail and and 23522 and and Nur Inshirah Naqiah Ismail and Zanariah Abdul and Majid and and 23523 and and Zanariah Abdul Majid and Norazak and Senu and and 23524 and and Norazak Senu}, title = {Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {5}, pages = {1138--1160}, abstract = {

Neutral Delay Differential Equation (NDDE) is a differential problem that has regularly existed in numerous occurrences and has represented a significant role in dealing with real-life phenomena, especially on their application in biological and physiological processes. A fifth-order two-point hybrid implicit multistep block method (2PIH5) has been formulated in this research for the numerical solution of Neutral Delay Differential Equation (NDDE). A Taylor series interpolation polynomial has been implemented in the formulation of the proposed 2PIH5. The order, consistency, and zero-stability for 2PIH5 have been illustrated. The analyses of convergence and stability test have been performed and discussed. The initial value problems for the first-order NDDE with constant or proportional delay have been solved using the proposed block method. Some numerical results for the proposed method have been presented to prove the adaptability and applicability of the proposed method in solving NDDE. The proposed method is proved to be comparable with the other existing methods. It is assumed to be reliable and efficient for solving the first-order NDDE with constant or proportional delay.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0054}, url = {http://global-sci.org/intro/article_detail/aamm/20555.html} }
TY - JOUR T1 - Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method AU - Ismail , Nur Inshirah Naqiah AU - Majid , Zanariah Abdul AU - Senu , Norazak JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1138 EP - 1160 PY - 2022 DA - 2022/06 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0054 UR - https://global-sci.org/intro/article_detail/aamm/20555.html KW - Constant delay, hybrid method, multistep block method, neutral delay differential equation, proportional delay. AB -

Neutral Delay Differential Equation (NDDE) is a differential problem that has regularly existed in numerous occurrences and has represented a significant role in dealing with real-life phenomena, especially on their application in biological and physiological processes. A fifth-order two-point hybrid implicit multistep block method (2PIH5) has been formulated in this research for the numerical solution of Neutral Delay Differential Equation (NDDE). A Taylor series interpolation polynomial has been implemented in the formulation of the proposed 2PIH5. The order, consistency, and zero-stability for 2PIH5 have been illustrated. The analyses of convergence and stability test have been performed and discussed. The initial value problems for the first-order NDDE with constant or proportional delay have been solved using the proposed block method. Some numerical results for the proposed method have been presented to prove the adaptability and applicability of the proposed method in solving NDDE. The proposed method is proved to be comparable with the other existing methods. It is assumed to be reliable and efficient for solving the first-order NDDE with constant or proportional delay.

Nur Inshirah Naqiah Ismail, Zanariah Abdul Majid & Norazak Senu. (2022). Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method. Advances in Applied Mathematics and Mechanics. 14 (5). 1138-1160. doi:10.4208/aamm.OA-2020-0054
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