A Class of One-Step Hybrid Third Derivative Block Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations

In this paper, we consider the development of a class of one-step hybrid third derivative block method with three off-grid points for the direct solution of initial value problems of second order Ordinary Differential Equations. We adopted method of interpolation and collocation of power series approximate solution to generate the continuous hybrid linear multistep method, which was evaluated at grid points to give a continuous block method. The discrete block method was recovered when the continuous block method was evaluated at selected grid points. The basic properties of the method was investigated and was found to be zero-stable, consistent and convergent. The efficiency of the method was tested on some stiff equations and was found to give better approximation than the existing method, which we compared our result with.