Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method

Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method

Year:    2022

Author:    Nur Inshirah Naqiah Ismail, Zanariah Abdul Majid, Norazak Senu

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2020-0054

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 1138–1160

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Constant delay hybrid method multistep block method neutral delay differential equation proportional delay.

Author Details

Nur Inshirah Naqiah Ismail

Zanariah Abdul Majid

Norazak Senu

  1. 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.

    Malaysian Journal of Mathematical Sciences, Vol. 17 (2023), Iss. 3 P.487

    https://doi.org/10.47836/mjms.17.3.15 [Citations: 0]
  2. Numerical Solution on Neutral Delay Volterra Integro-Differential Equation

    Ismail, Nur Inshirah Naqiah | Abdul Majid, Zanariah

    Bulletin of the Malaysian Mathematical Sciences Society, Vol. 47 (2024), Iss. 3

    https://doi.org/10.1007/s40840-024-01683-7 [Citations: 0]