Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method (Advances in Applied Mathematics and Mechanics, 2022)
Neutral Delay Differential Equation (NDDE) is a differential problem thathas regularly existed in numerous occurrences and has represented a significant rolein dealing with real-life phenomena, especially on their application in biologicaland physiological processes. A fifth-order two-point hybrid implicit multistep blockmethod (2PIH5) has been formulated in this research for the numerical solution ofNeutral Delay Differential Equation (NDDE). A Taylor series interpolation polynomialhas been implemented in the formulation of the proposed 2PIH5. The order, consistency, and zero-stability for 2PIH5 have been illustrated. The analyses of convergenceand stability test have been performed and discussed. The initial value problems forthe first-order NDDE with constant or proportional delay have been solved using theproposed block method. Some numerical results for the proposed method have beenpresented to prove the adaptability and applicability of the proposed method in solving NDDE. The proposed method is proved to be comparable with the other existingmethods. It is assumed to be reliable and efficient for solving the first-order NDDEwith constant or proportional delay.