Formulation and Implementation of Obreckoff's-Type Optimized Hybrid Block Method for the Solution of Second Order Ordinary Differential Equation Using Free Parameter Off-Grid Points

This paper examines the formulation and development of Obrechkoff-type three-step optimized block schemes for solving second-order initial value problems (IVPs) of ordinary differential equations. In the derivation of the method, the assumed power series is interpolated at and while the second derivative is collocated at all grid and off-grid points in the interval of consideration. The method's relevant properties were examined and found to be zero stable, consistent and convergent. The application of the method to some second-order initial value problems shows the derived method performed better in terms of accuracy and effectiveness; outperforming some existing methods when compared.