Special multistep methods based on numerical differentiation for solving the initial value problem

In this paper, methods based on numerical differentiation and their regions of absolute stability of some classes of special multistep methods are derived. Some of the methods given in Henrici [P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, Wiley, 1962] and some methods derived in this paper are applied to solve a second-order initial value problem hence establishing the superiority of the methods derived in this paper.