Numerical solution for neutral delay differential equaions of constant or proportional type using hybrid block method

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.

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