keywords: Collocation & interpolation, efficiency, hybrid block method, initial value problems
An efficient hybrid block method with variable step size for solving second-order nonlinear initial value problems (IVPs) is proposed in this paper. The scheme was developed through collocation and interpolation of power series approximate solution to give a continuous linear multistep method. The evaluation of the continuous method at the grid and off grid points produced the discrete block method. To validate the proposed method, the fundamental properties of the block method are examined. The accuracy of the developed method is confirmed by assessing it with the existing methods to solve three non-linear second order initial value problems and the outcome proved that the 1-point hybrid block method is efficient and appropriate for integrating second-order initial value problem.