Order Conditions of a Class of Three-step Hybrid Methods for y 00 = f(x, y)

Abstract

A theoretical approach of B-series is used to analyze the convergence and order of convergence of a newly introduced class of three-step hybrid methods for integrating systems of special second order ordinary differential equations (ODEs). A straightforward technique that generates algebraic order conditions, which is easier to handle than the well known Taylor series technique, is presented. The validity of the order conditions is tested by deriving a fourth order method and compared with existing methods in the literature.