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 - <p style="text-align: justify;">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.</p>