A Class of Hybrid Linear Multistep Methods for Solving Initial Value Problems of Second Order Ordinary Differential Equations

Abstract

In this paper, two - step hybrid numerical methods for direct solution of initial value problems of second order ordinary differential equations are proposed in this study. Chebyshev polynomials of the first kind are used as basic function for the approximate solution. The collocation and interpolation equations are generated at both grid and off-grid points for step number k=2. The resulting methods are consistent and and zero stable. The main predictors having the same order with the main method are developed for the implementation of the methods. The comparison shows a better performance than the existing methods.