Implementation of Two-step Hybrid Block Adams Moulton Solution Methods for First Order Delay Differential Equations

Abstract

In this paper, Hybrid Block Adams Moulton Methods for step number k = 2 merged with two and three off-grid points were obtained and implemented in solving first order delay differential equations without the use of interpolation condition in evaluating the delay expression. The discrete schemes of these off-grid hybrid block methods were assessed through the continuous development of the linear multistep collocation method using a matrix conversion formula. The results obtained after the implementation of the proposed method in for numerical experiment of some first-order DDEs, the BHAMM2 schemes performed better and faster in satisfying the axioms for convergence and region of absolute stability than the BHAMM3 schemes at fixed step size z when examined with other existing methods.