EFFECT OF INTERPOLATION POINTS ON STOMER - COWELL METHODS.

Abstract

This research work considered three – quarter step hybrid method for the solution of second order differential equations. In order to develop the methods, collocation and interpolation are carried out using power series as the basis function for the approximate solution of the differential equation. The Stomer - Cowell approach was adopted to develop three of the schemes while the other three schemes were obtained by interpolating the approximate solution at the first grid point and one – off grid point. The order, zero stability, consistency and convergence of the hybrid methods were determined. Taylor’s series algorithm of the same order as the schemes was used to implement the schemes. The schemes were used to solve linear and non-linear second order ordinary differential equations, and the results compared favorably with the results of existing methods in literature.