A hybrid two-step method for direct solutions of general second order initial value problem

Abstract

The study is concerned with the development of a two-step hybrid linear multi-step method for direct solution of general second order initial value problem. Power series is adopted as the basis function, and the differential system arising from it are collocated at all grid and off-grid points, while the approximate solution is interpolated at the selected points. The scheme developed is tested for consistency and zero stability, and it was found to be convergent.The scheme is expanded term by term by Taylor series approach, also the efficiency of the methods is tested on some test problems, and the accuracy is compared with some existing result in literature.