A Class of Seventh Order Hybrid Extended Block Adams Moulton Methods for Numerical Solutions of First Order Delay Differential Equations

Abstract

This paper considers the computational solution of some first order delay differential equations (DDEs) using a class of seventh order Hybrid Extended Block Adams Moulton Methods (HEBAMM) without the application of interpolation techniques in evaluating the delay term. The delay term was evaluated by a valid expression of sequence. By matrix inversion techniques, the discrete schemes of the proposed method were obtained through its continuous derivations with the help of linear multistep collocation procedure. The convergence and stability analysis of the method were investigated. After the demonstration of the proposed method in solving some first order DDEs, it was observed that the higher step number k = 4 integrated with a hybrid extended future point performed better and faster in terms of efficiency, accuracy, consistency, convergence, region of absolute stability and Central Processing Unit Time (CPUT) than the lower step numbers k = 3 and 2 integrated with hybrid extended future points when compared with the exact solutions and other existing methods at fixed step size .