Multistep Methods for a Class of Higher Order Differential Problems: Convergence and Error Bounds

Abstract

In this paper multistep methods for higher order differential systems of the type $Y^{(r)}=f(t,Y)$ are proposed. Such methods permit the numerical solutions of initial value problems for such systems, providing error bounds and avoiding the increase of the computational cost derived from the standard approach based on the consideration of an equivalent extended first order system.