An Eight Order Two-Step Taylor Series Algorithm for the Numerical Solutions of Initial Value Problems of Second Order Ordinary Differential Equations

摘要

Our focus is the development and implementation of a new two-step hybrid method for the direct solution of general second order ordinary differential equation. Power series is adopted as the basis function in the development of the method and the arising differential system of equations is collocated at all grid and off-grid points. The resulting equation is interpolated at selected points. We then analyzed the resulting scheme for its basic properties. Numerical examples were taken to illustrate the efficiency of the method. The results obtained converge closely with the exact solutions.