An Implicit Two-Step One Off-Grid Point Third Derivative Hybrid Block Method for the Direct Solution of Second-Order Ordinary Differential Equations

In this paper, we propose an implicit two-step third derivative hybrid block method with one off-step point for the direct solution of second order Ordinary Differential Equations. We adopted the method of interpolation and collocation of power series approximate solution to generate the continuous hybrid linear multistep method, which was evaluated at non-interpolated step points to give a continuous block method. The discrete block method was recovered when the continuous block method was evaluated at all step points. The basic properties of the method were investigated and the method 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 methods with which we compared our results.